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VBQ Probability
NCERT Solutions For Class 10 Maths
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Areas Related to Circles CBSE Class 10 Maths Higher Order Thinking Skills Questions and Answers
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NCERT Solutions For Class 10 Maths
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MuItipIe Choice with ONE correct answer
1.A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement(s) from the following [1985-2 marks]
a)The entire rod is at same electric potential.
b)There is an electric field in the rod
c)The electric potential is highest at the centre of the rod and increases towards its ends.
d)The electric potential is lowest at the centre of the rod and decreases towards its ends
Ans.(b) Let the metal rod AB move parallel to x-axis. Let the uniform magnetic field point in positive z- direction. The free electrons of the metal rod will experience magnetic force towards B. So there will be excess of electrons on B- end and shortage of electrons on A-end. The end A becomes positively charged and the end B becomes negatively charged. An electric field is therefore setup in the metal rod. Option (b) is correct.
2.A thin circular ring of area A is held perpendicular to a uniform magnetic field of induction B. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is R. When the ring is suddenly squeezed to zero ‘area, the charge flowing through the galvanometer is [1995]
Ans.
3.A thin semicircular conducting ring of radius R is falling with its plane vertical in horizontal magnetic induction g , At the position MNQ the speed of the ring is v, and the potential difference developed across the ring is
Ans.(d) At the position MNQ, the ring is at the point of moving out of the magnetic field. Its speed of fall is v. Due to fall, the flux associated with the ring changes. An emf is therefore induced in the ring.
4.Two identical circular loops of metal wire are lyingon a table without touching each other, Loop-A carries a current which increases with time. In response, the loop-B. [JEE ’99 2 Marks]
a)remains stationary
b)is attracted by the loop-A
c)is repelled by the loop-A
d)rotates about its CM, with CM fixed
Ans.(c)When the current in loop A increases, its magnetic field in the surrounding space increases. The flux linked with loop B therefore increases. An emf is induced in B. Under Lenz’s law, the current flows in B opposite to that in A. Due to opposite directions of currents in A and B, loop B is repelled by loop A.
5.A coil of inductance 8.4 mil and resistance 6W is connected to a 12V battery. The current in the coil is 1.0 A at approximately the time [JEE’99-2 Marks]
a) 500 s
b) 25 s
c)35 ms
d)1 ms
Ans.
6.A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as showm in the figure. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region. [2000-2 marks]
Ans.
7.
Ans.
8.A metallic square loop ABCD is moving in its own plane with velocity v in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric field is induced. [2001-2 marks]
Ans.
Ans.(a)When current flows in one coil, the flux associated with the other coil depends upon its area receiving the flux. This is maximum in case (a) and so their mutual inductance will be maximum in situation (a).
Ans.(d)When switch S is closed a magentic field is set up in the space around P. The field lines threading Q increase in the direction from right to left and that field strength increases with time. According to Lenz’s law, IQ1 should therefore flow in anticlockwise direction as seen by E. Reverse is the case when S is opened. IQ2 will be clockwise.
11. A short -circuited coil is placed in a time varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be [JEE 2002(Scr), 2 Marks]
a) halved
b) the same
c) doubled
d) quadrupled
Ans.(b)Current is induced in the short-circuited coil due to the imposed time-varying magentic field.
Ans.
13. A small bar magnet is being slowly inserted with constant velocity inside a solenoid as shown in figure. Which graph best represents the relationship between emf induced with time? [2004- 2 M]
Ans.(c) As the bar magnet is inserted inside a solenoid, flux associated with the solenoid increases. Induced emf is negative.
This emf increases as more length of the bar magnet is inserted in solenoid. Then emf starts decreasing. Polarity of emf will be opposite when the magnet enters and leaves the coil.
14.A capacitor is charged using an external battery with a resistance x in series The dashed line shows the variation on In I with respect to time. If the resistance is changed to 2x, the new graph will be [2004 – 2 Marks]
Ans.
15. A 4pF capacitor and a resistance of 5MQ are in series with 12V battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given In (2) = 0.693]. [2005-2 marks]
Ans.
16.An infinitely long cylinder is kept parallel to auniform magnetic field g directed along positive z axis. The direction of induced current as seen from the z axis will be [2005 – 2 Marks ]
a).zero
b).anticlockwise of the +ve zaxis
c).clockwise of the + ve zaxis
d).along the magnetic field
Ans.(a) The cylinder is not moving in stationary magnetic field. No emf is induced.The magentic filed applied to stationary cylinder is neither moving nor changing.No emf is induced in the cylinder.No current is induced in the cylinder.Induced current = zero.
Ans.
18.An AC voltage source of variable angular frequency CO and fixed amplitude V0 is connected to series with a capacitance C and an electric bulb of resistance R (inductance zero). When CO is increased)
a) the bulb glows diammer
b) the bulb glows brighter
c) total bulb glows brighter
d) total impedance of the circuit increases
Ans.
19. The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. and I2 are the currents in the segments ab and cd. Then, [2009]
Ans.(d)Since the field is increasing, the flux region is increasing; the induced current (by Lenz law) should flow in an anticlockwise sense around the boundary of the shaded region.
Multiple Choice with ONE or MORE THAN ONE correct answers
20.A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction ~g, constant in time and space, pointing perpendicular and into the plane of the loop exists every where. The current induced in the loop is [1989-2 marks]
Ans.The square loop moves in its plane.A uniform magnetic induction exists in the plane of the loop. Hence change in magnetic flux is zero. Induced current in the loop = zero.
21. Two different coils have self inductances Lj = 8mH and L2= 2mH. The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the power given to the two coils is the same. At that time, the current, the induced voltage and the energy stored in the first coil are ip Vj and W( respectively. Corresponding values for the second coil at the same instant are i2, v2 and W2 respectively. Then:
Ans.
22. A small square loop of wire of side l is placed inside a large square loop of wire of side L(L»Z). The loops are co-planar & their centres coincide. The mutual inductance of the system is proportional to [1998- 2 Marks]
Ans.
23.A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant, uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement(s) from the following
a)the entire rod is at the same electric potential
b)There is an electric field in the rod
c)The electric potential is highest at the centre of the rod & decreases towards its ends
d)The electric potential is lowest at the centre of the rod & increases towards its ends
Ans.
24. A field line is shown in the figure. This field cannot represent
a)magnetostatic field
b)electrostatic field
c)induced electric field
d)gravitational field
Ans.
25.Two metallic rings A and B, identical in shape and size but having different resistivities pA and pB, are kept on top of two identical solenoids as shown in the figure. When current I is switched on in both the solenoids in identical manner, the rings A and B jump to heights hA and hB, respectively, with hA > hB. The possible relation(s) between their resistivities and their masses mA and mB is (are) [2009]
Ans.
26.A series R-C circuit is connected to AC voltage source. Consider two cases ; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage Vc across the capacitor are compared in the two cases. Which of the following is / are true ?
Ans.
Assertion – Reasoning type
Instructions :The following question contains statement-I (assertion) and statement -2 (reason) of these statements, mark correct choice if
a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statement-l and2 are true and statement-2 is not a correct explanation for statement-1
c)Statement-1 is true, statement-2 is Base
d)Statement-1 is false, statement-2 is true.
27.Statement – 1 : A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure.The ring can float at a certain height above the coil. [2007]
Because Statement – 2 : In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.
a)Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explantation for Statement- 1.
b)Statement – 1 is True, Statement – 2 is True; Statement -2 is NOT a correct explanation for Statement-1.
c)Statement – 1 is True, Statement – 2 is False.
d)Statement – 1 is False, Statement -2 is True.
Ans.(a) The induced current in the ring will interact with horizontal component of magnetic field and both will repel each other. This repulsion will balance the weight of the ring.
Comprehension based question
Read the passage given below and answer the questions that follow :
In the given circuit the capacitor (C) may be charged through resistance R by battery V by closing switch S1. Also when S1 is opened and S2 is closed the capacitor is connected in series with inductor (L).
Ans.
Ans.(d) When the capacitor gets fully charged S is opened and S2 is closed. Capacitor gets discharged.
Ans.
Matching type
31.You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the furs two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current I (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage and V2. (indicated in circuits) are related as shown in Column I. Match the two
Ans.
32.Column I gives certain situations in whcih a straight metallic wire of resistance R is used and column II gives some resulting effects. Match the statements in column I with the statements in column II. [2007-6 marks]
Ans.
Subjective / Numerical integer type
33.A current from A to B is increasing in magnitude. What is the direction of induced current, in the loop as shown in the figure? [1979]
Ans.The direction of the induced current is as shown in the figure, according to Lenz’s law which states that the indeed current flows always in such a direction as to oppose the change which is giving rise to it.
34.The two rails of a railway track, insulated from each other and the ground, are connected to a millivolt meter. What is the reading of the milli voltmeter when a train travels at a speed of 180 km/hour along the track, given that the horizontal components of earth’s magnetic field is 0.2 x 10-4 weber / m2 and the rails are separated by 1 metre? [1981 – 4 Marks]
Ans.
35.Three ideitical closed coils A, B and C are placed and C cairy equal currents as shown in fig. Coils B and C are fixed in position and coil A is moved direction of the induced current in the diagram.[1982 – 2 Marks]
Ans.Coils B and C are fixed. When the coil A is moved towards the parallel coil B, at uniform speed, the magnetic flulx linked with B changes. An induced e.m.f. is setup in B and an induced current flows in B.
Under the phenomenon of induction, the induced current in 5 will flow so as to oppose the cause which produces it.Hence current in 5 will be in a direction opposite to that of . The direction of induced current is marked in the figure.
36.A sqiare metal wire loop of side 10 cm and resistaice 1 ohm is moved with a constant velocity v0in a uniform magnetic field of induction B = 2 weber / m2 as shown in the figure. The magnetic field lines are perpendicular to the plane of the loop (directed into the paper). The’ loop is connected to a network of resistors each of value 3 ohm. The resistances of the lead wires OS and PQ are negligible. What should be the speed of the loop so as to have a steady current of 1 milli ampere in the loop? Give the direction of current in the loop. [1983-6 marks]
Ans.
37.Space is divided by the line AD into two regions. Region I is field free and the Region II has a uniform magnetic field B directed into the plane of the paper. ACD is a semicircular conducting loop of radius r with centre at O, the plane of the loop being in the plane of the paper. The loop is now made to rotate with a constant angular velocity u about an axis passing through O and the perpendicular to the plane of the paper. The effective resistance of the loop is R. [1985-6 marks]
i)Obtain an expression for the magnitude of the induced current in the loop.
ii)Show the direction of the current when the loop is entering into the Region II.
iii)Plot a graph between the induced emf and the time of rotation for two periods of rotation.
Ans.
Ans.
Ans.
Ans.
41.Two parallel vertical metallic rails AB & CD are separated by 1 m. They are connected at two ends by resistance R1 & R2 as shown in the figure. A horizontal metallic bar L of mass 0.2 kg slides without friction, vertically down the rails under the action of gravity. There is a uniform horizontal magnetic field of 0.6T perpendicular to the plane of the rails. It is observed that when the terminal velocity is attained, the powers dissipated in R1 & R2 are 0.76 W & 1.2 W respectively. Find the terminal velocity of bar L & the values of R1 & R2.[1994, 6 Marks]
Ans.
42.A metal rod OA of mass m & length r is kept rotating with a constant angular speed v in a vertical plane about a horizontal axis at the end O. The free end A is arranged to slide without friction along a fixed conducting circular ring in the same plane as that of rotation. A uniform & constait magnetic induction B is applied perpendicular & into the plane of rotation as shown in figure. An inductor L and an external resistance R are connected through a switch S between the point O & a point C on the ring to form an electrical circuit. Neglect the resistance of the ring and the rod. Initially, the switch is open. [1995-10 Marks]
Ans.OA is metal rod which rotates with a constant angular speed cc . The free end A of rod OA slides along a fixed conducting circular ring, g is the uniform and constant magnetic induction applied perpendicular and into the plane of rotation of the rod.(a) Induced emf across switch S :
43.A solenod has an inductance of 10 Henry & a resistance of 2 W. It is connected to a 10 volt battery. Sow long will it take for the magnetic energy to reach 1/4 of its maximum value ?[1996-3 Marks]
Ans.
44.An infiritesimally small bar magnet of dipole moment M is pointing and moving with the speed v in the x-direction. A small closed circular conducing loop of radius a and negligible self- inductance lies in the y-z plane with its centre at x = 0, aid its axis coinciding with the x-axis. Find the force opposing the motion of the magnet, if the resistance of the loop is R. Assume that the distant of x of the magnet from the centre of the loop s much greater than a. [1997- 5 Marks]
Ans.A closed circular conducting loop lies in the y — z plane with its centre at x = 0 . A small bar magnet moves with the speed v in the x— direction.Magnetic lines of the moving bar magnet thread the loop. An induced emf is therefore developed in the loop and an induced current flows in the closed loop.
Positive sign of force denotes repulsion between the magnet and the coil.
45.A par of parallel horizontal conducting rails of neglgible resistance, shorted at one end is fixed on a table. The distance between the rails is L. A concucting massless rod of resistance R can slide on he rails frictionlessly. The rod is tied to a masless string which passes over a pulley fixed to he edge of the table. A mass m, tied to the otler end of the string, hangs vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate:
i)the terminal velocity achieved by the rod.
ii)the acceleration of the mass at the instant when the velocity of the rod, is half the terminal velocity.[1997 – 5 Marks]
Ans.
Ans.
Ans.
48.A thermocole vessel contains 0.5 kg of distilled water at 30° C • A metal coil of area 5 x 103m2 number of turns 100, mass 0.06 kg and resistance 1.6 ohms is lying horizontally at the bottom of the vessel. A uniform time varying magnetic field is setup to pass vertically through the coil at time t=0. The field is first increased from zero to 0.8T at a constant rate between 0 and 0.2s and then decreased to 0 and the same rate between 0.2 and 0.4s. This cycle is repeated 12000 times. Make sketches of the current through the coil and the power dissipated in the coil as function of time for the first two cycles. Clearly indicate the magnitudes of the quantities on the axes. Assume that no heat is lost to the vessel or the surroundings. Determine the final temperature of the water under thermal equilibrium. Specific heat of metal = 500 J kg-1K-1 and the specific heat of water =4200 J kg-1K-1. Neglect the inductance of the coil. [2000-10 marks]
Ans.
49.An inductor of inductance L = 400 mH and resistors of resistance R1 = 2W and R2 = 2W are connected to a battery of e.m.f. E = 12V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at time t = 0. What is the potential drop across L as a function of time? After the steady state is reached, the switch is opened. What is the direction and the magnitude of current through R1 as a function of time?[2001-5 Marks]
Ans.
50.A rectangular loop PQRS, made from a uniform wire, has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y — axis (see figure).
Ans.A loop PQRS is held in the x— y plane. It is free to rotate about arm PQ which remains hinged along y — axis. A current / is passed through it. When the loop is released, it stays in horizontal position in equilibrium.(a) Direction of current I in PQ .Let the direction of current I in PQ be from P to Q in the wire PQ. The loop develops a mag¬netic moment = M
51.A metal bar AB can slide on two parallel thick metallic rails separated by a distance l. A resistance R and an inductance L are connected to the rails as shown in the figure. A long straigit wire carrying a constant current I0 is placed in tie plane of the rails and perpendicular to them as shown. The bar AB is held at rest at a distance x1 from the long wire. At t=0, it is made to slide 01 the rails away from the wire. [1002- 5 Marks]
Ans.
52.
Ans.
53.In the figure both cells A and B are of equal emf E. Find R for which potential difference across battery A will be zero, long time after the switch S is closed. Internal resistance of batteries A and B are r1 and r2 respectively, ( r1 > r2).[2004 – 4 Marks]
Ans.The circuit contains resistances, inductance and capacitance as shown in the figure.
When current flows for a long time the capacitor will be fully charged. Resistance across capacitor becomes infinite and no current passes through it. Resistance across inductor is zero for D.C. and the whole current passes through it.
Ans.
Ans.
True/ False type
56.An e.m.f. can be induced between the two ends of a straight copper wire when it is moved through a uniform magnetic field. [1980]
Ans.True : It the conductor cuts the lines of force.
57.A coil of metal wire is kept stationary in a non uniform magnetic field. An emf is induced in the coil. [1986-3 marks]
Ans.false :The coil of metal wire is stationary in a non-uniform magnetic field. The magnetic flux linked with the coil does not change.An emf is therefore not induced in the coil.The statement is false.
58.A conducting rod AB moves parallel to the x-axis (see figure) in a uniform magnetic field pointing in the positive z-direction. The end A of the rod gets positively charged. [1987-2 Marks]
Ans.false :The coil of metal wire is stationary in a non-uniform magnetic field. The magnetic flux linked with the coil does not change. An emf is therefore not induced in the coil. The statement is false.
Therefore at g, there will be an excess of elections and at 4 there will be a deficiency of electrons. The end A of the rod gets positively charged because deficiency of electrons means a positive charge. The statement is true.
Fill in blanks
59.A uniformly wound solenoidal coil of self inductance 1,8 xl0-4 henry and resistance 6 ohm is broken up into two identical coils. These identical coils are then connected in parallel a cross a 15 volt battery of negligible resistance. The time constant for the current in the circuit is second and the steady state current through the battery is……………..ampere. [1989-2 marks]
Ans.
60.In a straight conducting wire, a constant current is flowing from left to right due to a source of emf. When the source is switched off, the direction of the induced current in the wire will be………………………………….[1993-1 mark]
Ans.When the source is switched off, current flowing from left to right in the conducting wire decreases to zero. According to Lenz’s law’, induced currrent will oppose the cause. Consequently the direction of induced current in the wire will be from left to right.
Ans.
JEE Main Home Maths Physics Chemistry
The post JEE Main Previous Year Papers Questions With Solutions Physics Electro Magnetic Induction appeared first on Learn CBSE.
Multiple Choice with ONE correct answer
1.A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 volt. The potential at the centre of the sphere is [1983- Imark]
a) zero b) 10 volt
c)same as at a point 5 cm away from the surface
d)same as at a point 25 cm away from the surface
Ans.(b) Electric potential at any point inside a hollow metal sphere is constant. The potential at the surface is 10 volt. The potential at the centre will also be 10
2.Two point charges +q and -q are held fixed at (-d,0) and (d,0) respectively of a x-y coordinate system. Then [1995-2 marks]
a)The electric field E at all points on x-axis has the same direction
b)Electric field at all points on y-axis is along x-axis
c)Work has to be done in bringing a test charge from infinity to the origin
d)The dipole moment is 2qd along the x-axis
Ans.(b) (a) E on x-axis E will not have same direction along entire x-axis. Option (a) is incorrect.
For – d < x < d, the field is along +x-axis For all other points, E is along negative x-axis
b)Electric field at P, a point on y-axis is parallel to x-axis. It is not along x-axis itself. It is nearest to correct answer.
c)Electric potential at origin is zero No work has to be done in bringing a test charge from infinity to the origin. Option (c) is incorrect
d)The dipole moment is directed from -q charge to +q charge, along negative direction, of x-axis.
.•. Dipole moment = -2qd along x-axis.
The option is incorrect.Hence option (b) is nearest to correct answer.
3.A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is similarly charged to a potential difference 2V. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is [1995-2 marks]
Ans.
4.An electron of mass me, initially at rest, moves through a certain distance in a uniform electric field in time tr A proton of mass mp) also initially at rest, takes time t2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of t, /1, is nearly equal to[1997-1 mark]
a) 1 b) (mp/me)1/2
c) (me/mp)1/2 d) 1836
Ans.
Ans.
Ans.(d) Resistor (R) and capacitor (C) are connected in parallel. They are connected across a 1.5 volt source of negligible resistance.Since the capacitor is directly connected to voltage source and there is no resistance in the path,
7.Two identical metal plates are given positive charges Q1 and Q2 (<Q1) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance C, the potential difference between them is [1999-2 marks]
a) (Q1+Q2)/(2C) b) (Q1+Q2)/C
c)(Q1-Q2)/C d) (Q1-Q2)/(2C)
Ans.
8.For the circuit shown in figure, which of the following statement is true ? [ JEE ’99, 2 ]
a)with S1 closed, V1 = 15 V, V2 = 20 V
b)with S3 closed, V1 = V2 = 25 V
c)with S1 & S2 closed, V1 = V2 = 0
d)with S1 & S3 closed, V1 = 30 V, V2 = 20 V
Ans.(d) No change of any potential across any capacitor will occur unless the two capacitors Cj and C2 are either connected in series or in parallel.Charges would be maintained as they are unless Sj, S2 and S3, all are closed.This condition is given in none of the options. Hence the potentials of C1 and C2 will be maintained as V1 = 30 volt and V2 = 20 volt, with S, and S3 closed.
9.Three charges Q, -i-q and -t-q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero
Ans.
10.A parallel plate capacitor of area A, Plate separation d and capacitance C is filled with three different dielectric materials having dielectric constant Kp K2 and K3 as shown in the figure. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant K is given by
Ans.
11.Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in [JEE 2001-1 mark]
Ans.(c) Electric lines of force do not end at positive charge as shown in (a). The option is therefore incorrect. Electric lines of force never form a closed loop. Options (b) and (d) are incorrect.Option (c) represents correct answer. Mutual repulsion between similar charges is depicted in figure.
12.Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is [2001-1 mark]
Ans.(a) Due to attraction of positive charge, the negative charge is bound and so it will not flow to capacitor B through the switch S.Option (a) represents the correct answer.
13.A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x-axis at x=+l cm and C be the point on the y-axis at Y=+l cm. Then the potentials at the points A,B and C satisfy. [2001-1 mark
a)VA<VB b)VA>VB c) VA<Vc d)VA>Vc
Ans.(b) Potential decreases as we move along the direction of electric field. The field E is uniform and runs patallel to x-axis.Any line perpendicular to x-axis is an equipotential line.
14.Two equal point charges are fixed at x = -a and x = +a on the axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x-axis, is approximately proportional to [JEE 2002-1 mark]
a)x b) x2 c) x3 d) 1/x
Ans.
15.Two identical capacitors, have the same capacitance C. One of them is charged to potential Vj and the other V2. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is[JEE 2002 (Scr), 3]
Ans.(c) When two capacitors joined together by connecting positive plate to positive plate and negative plate to negative plate, then the loss of mechanical energy or heat produced or work done to drive the change is given by
16.A metalic shell has a point charge q kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of force? [JEE’2003 (scr)]
Ans.(c) Field lines do not enter the metallic portion of the shell as field is zero inside the metal. Hence options (a) and (d) are incorrect.The field lines are normal to metal surface.Hence option (b) is incorrect.Both the conditions are satisfied in option (c), Hence (c) represents the correct answer.
17.Six charges of equal magnitude , 3 negative are to be placed on PQRSTU comers of a regular hexagon, such that field at the centre is double that of what it would have been if only one +ve charge is placed at R. [2004-1 mark]
Ans.
(c) According to option (c), the electric fields at O due to
i)P and S nullify each other
ii)Q and T nullify each other
iii)R and U add up to 2E
Hence option (c) represents the answer.
18.A Gaussian surface in the figure is shown by dotted line. The electric field on the surface will be [2004-1 mark]
Ans.(d) At any point over the spherical Gaussian msurface, net electric field is the vector sum of electric fields due to all the three charges +qp -q1 and q2.
19.Three infinitely long charge sheets are placed as shown in figure. The electric field at point P is [2005-1 mark]
Ans.(c) All the three charge sheets will produce electric field at P. The field will be along negative Z-axis.Hence
20.Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then. [2007-3 marks]
a)negative and distributed uniformly over the surface of the spher
b)negative and appears only at the point on the sphere closest to the point charge
c)negative and distributed non-uniformly over the entire surface of the sphere
d)zero
Ans. (d) When a positive point charge is placed outside a conducting sphere, a rearrangement of charge take place on the surface.But the total charge on the sphere is zero as no charge has left or entered the sphere.
21.A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. [2007-3 marks]
a)A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
b)A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
c)No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.
d)No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
Ans.(a) When a charge density is given to the inner cylinder, the potential developed at its surface is
different from that on the outer cylinder. This is because the potential decreases with distance for a
charged conducting cylinder when the point of consideration is outside the cylinder.
But when a charge density is given to the outer cylinder, it will change its potential by the same amount as that of the inner cylinder. Therefore no potential difference will be produced between the cylinders in this case.
22.A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is [2007-3 marks]
a)zero everywhere
b)non-zero and uniform
c)non-uniform
d)zero only at its center.
Ans.
Ans.It can be seen that potential at both points A and B are zero. When the charge is moved from A to B, work done by the electric field on the charge will be zero.
Ans.
25.A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K=2. The level of liquid is d/3 initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is [2008]
Ans
Ans.
27.Under the influence of the Coulomb field of charge +Q, a charge -q is moving around it in an elliptical orbit. Find out the correct statement(s). (2009)
a)The angular momentum of the charge -q is constant
b)The linear momentum of the charge -q is constant
c)The angular velocity of the charge -q is constant
d)The linear speed of the charge -q is constant
Ans.(a) The angular momentum of the charge -q is constant
28.A disk of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its centre at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = ±a/2, y = +a/2, z = +a/2. The electric flux through this cubical surface is(2009)
Ans.
29.Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q1 Q2, Q3, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then the ratio of the charges given to the shells, Q1 : Q2: Q3, is (2009)
a)1 : 2 : 3 b) 1 : 3 : 5 c) 1 : 4 : 9 d) 1 : 8 : 18
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Multiple Choice with ONE or More Than ONE correct answers
32.Two equal negative charge -q are fixed at points (0, -a) and (0, a) on y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will. [1984-2 marks]
a)execute simple harmonic motion about the origin
b)move to the origin remain at rest
c)move to infinity
d)execute oscillatory but not simple harmonic motion.
Ans.
33.A parallel plate air capacitor is connected to a battery. The quantites charge, voltage, electric field and energy associated with this capacitor are given by Q0,V0,E0 and U0 A dielectric slab is now introduced to fill the space between the plates with battery still in connection. The corresponding quantities now given by Q, V< E and U are related to the previous one as [1985-2 marks]
a)Q >Q0 b) V > V0 c) E >E0 d)U>U0
Ans.
34.A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to [1987-2 marks]
Ans.
35.A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles [1987-2 marks]
a)the charge on the capacitor increases
b)the voltage across the plates increases
c)the capacitance increases
d)the electrostatic energy stored in the capacitor increases.
Ans.
36.A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of -3Q, the new potential difference between the same two surfaces is [1989-2 marks]
a) V b) 2V c) 4V d) -2V
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38.A parallel plate capacitor of plate area A and plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q,E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted), and the workdone on the system, in question, in the process of inserting the slab, then [1991-2 marks]
Ans.
39.Two identical thin rings, each of radius R metre, are coaxially placed at a distance R metre apart. If Q1 coulomb and Q2 coulomb, are respectively the charges uniformly spread on the two rings, the work done in moving charge q from the centre of one ring to that of the other is [1992-2 marks]
Ans.
40.The magnitude of electric field E in the annular region of a charged cylindrical capacitor
a)Is same throughout [IIT’96, 2]
b)Is- higher near the outer cylinder than near the inner cylinder
c)Varies as (1/r), where r is the distance from axis
d)Varies as (1/r2), where r is the distance from axis
Ans.
41.A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s)
Ans.(d) The lines of force never enter a metallic sphere because intensity is zero inside a conductor/metal. Hence options (b) and (c) are incorrect.The lines of force are at normal to the surface. Hence option (a) is incorrect.Option (d) represents the correct answer.
42.A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x=0 and positive plate is at x=3d. The slab is equidistant from the plates. The capacitor is given some charge. As one goes from 0 to 3d, [1998-2 marks]
a)the magnitude of the electric field remains the same
b)the direction of the electric field remains the same
c)the electric potential increases continuously
d)the electric potential increases at first, then decreases and again increases.
Ans.b)The direction of electric field remains the same. Option (b) is therefore correct.
c)Electric field lines always flow from higher potential to lower potential. The electric potential V, therefore, increases continuously as one goes from x = 0 to x = 3d. OA || BC Slope of (OA) > slope of AB Option (c) is correct.
d)The option is incorrect. Refer to figure (iii)
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Ans.(c), (d) Points A and B lie on the ellipsoidal cavity carved within a perfect conductor. Since the
potential of all points which lie on the conductor,is same,the potentials at A and B are same.
Potential at A=Potential at B Option (c) is correct.According to Gauss theorem,Hence option (d) is correct.Options (a) and (b) are incorrect as the cavity is ellipsoidal. It may, however, be noted that options (a) and (b) hold good in case of a spherical caivty.
47.spherical symmetric charge system is centred at origin. Given, electric potential [2006-5 marks]
Ans.
48.A few electric field for a system of two charges Q, and Q2 fixed at two different points on the x-axis are shown in the figure. These lines susggest that
Ans.(a), (d) Number of lines of force is directly pro- portional to the magnitude of the charge so |Qi|>|Q2|
At null point where E = 0, there will be no lines of force of only the given two charges are considered, there is a chance of getting E = 0 to the right of Q2 (Null point will be closer to the charge having small magnitude)
49.A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (<RA) are kept far apart and each is given charge ‘+Q’. Now they are connected by a thin metal wire. (2011)
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50.Which of the following statement(s) is / are correct
a)If the electric field due to a point charge varies as r2 5 instead of r2, then the Gauss law will still be valid (2011)
b)the gauss law can be used to calculate the field distribution around an electric
c)If the electric field between two point charges is zero some where, then the sign of the two charges is the same
d)the work done by the external force in moving a unit positive charge from point A at potential VA to potential VB is (VB – VA)
Ans.
Assertion – Reasoning type
Instructions : The following question contains statement-I (assertion) and statement -2 (reason) of these statements, mark correct choice if
a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statement-1 and2 are true and statement-2 is not a correct explanation for statement-1
c)Statement-1 is true, statement-2 is flase d) Statement-1 is false, statement-2 is true.
51.Statement -1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
Statement -2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the
Ans.(b) Statement -1 is true, you all are familiar with this convention.Statement – 2 is true. You all know this, recall the shell theorem.But statement -2 is not the correct explanation of statement – 1.
Comprehension based question
Read the passage given below and answer the questions that follow
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density p(r) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.
52.The electric field at r = R is
a) independent of a b) directly proportional to a c) directly proportional to a2 d) inversely proportional to a
Ans.(a) Electric field at a distance R from the centre of the nucleus es,
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54.The electric field within the nucleus is generally observed to be linearly dependent on r. This implies
a)a=0 b)R/2 c)a=R d)2R/3
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Matching type
Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column – II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (Potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and p be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current. [2009]
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56.A rigid insulated wire frame in the form of a right angled triangle ABC, is set in a vertical plane as shown in fig. Two beads of equal masses m each and carrying charges qj and q7 are connected by a cord of length / and can slide without friction on the wires.Considering the case when the beads are stationary determine [1978]
Ans.(a) Consider first the equilibrium of bead at P, having charge qr Different forces acting on it are shown in the figure. If the charges qj and q2 are similar in nature, then electric force F will be repulsive and is given by
57.A charged particle is free to move in an electric field. Will it always move along an electric line of force? [1979]
Ans.It moves along the line of force only if it is straight.
58.A charge Q is distributed over two concentric hollow spheres of radii r and R (>r) such that the surface densities are equal. Find the potential at the common centre. [1981-3 marks]
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59.The figure shows two identical parallel plate capacitors connected to a battery with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant (or relative permittivity) 3. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.
Ans.
Ans.The moving charge -q has potential and kinetic energies while at C and at D. The sum of the two energies at C and D remains constant.
61.Three point charges q, 2q and 8q are to be placed on a 9 cm long straight line. Find the positions where the charges should be placed such that the potential energy of this system is minimum. In this situation, what is the electric field at the position of the charge q due to the other two charges? [1987-7 marks]
Ans.The potential energy will be minimum when the two bigger charges are located at maximum distance in the system. Let x cm = x x 10-2m, be the distance between 2q and q.
62.Three particles, each of mass lg and carrying a charge q, are suspended from a common point by insulated massless strings, each 100 cm long. If the particles are in equilibrium and are located at the comers of an equilateral triangle of side length 3cm, calculate the charge q on each particle. (Take g = 10m/s2) [1988-5 marks]
Ans.Each particle of mass m and charge q is suspended by a 100 cm long string, m=l gram. They are located at corners of an equilateral triangle of sidelength 3 cm. Three forces act on each particle.
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64.Two fixed charges -2Q and Q are located at the points with coordinates (-3a, 0) and (+3a, 0) respectively in the x-y plane. [1991-4+2+2 marks]
a)Show that all points in the x-y plane, where the electric potential due to the two charges is zero, lie on a circle. Find its radius and the location of its centre.
b)Give the expression V(x) at a general point on the x-axis and sketch the function V(x) on the whole x-axis
c)If a particle of charge +q starts from rest at the the centre of the circle, show by a short quantitative argument that the particle eventually crosses the circle. Find its speed when it does so.
Ans.Charge (-2Q) is located at (-3a, 0) in x-y plane Charge (Q) is located at (+3a, 0) in x-y plane, a) Locus of zero potential:Let P be a general point, denoted by (x,y), wher potential due to the two charges is zero.
65.a) A charge of Q coulomb is uniformly distributed over a spherical volume of radius R metre. Obtain an expression for the energy of the system.
b)What will be the corresponding expression for the energy needed to completely disassemble the planet earth against the gravitational pull amongest its constituent particles?
Assume the earth to be a sphere of uniform mass density. Calculate this energy, given the product of the mass and the radius of the earth to be 2.5 x l031kg.m.
c)If the same charge of Q coulomb as in part a) above is given to a spherical conductor of the same radius R, what will be energy of the system? [1992-10 marks]
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66.Two parallel plate capacitors A & B have the same separation d = 8.85 x 10-4 m between the plates. The plate area of A & B are 0.04 m2 & 0.02 m2 respectively. A slab of di-electric constant (relative permittivity) K=9 has dimensions such that it can exactly fill the capacitor between the plates of [1999-7]
i)the di-electric slab is placed inside A as shown in the figure (a) A is then charged to a potential difference of 110 volt. Calculate the capacitance of A and the energy stored in it.
ii)the battery is disconnected & then the di-electric slab is moved from A . Find the work done by the external agency in removing the slab from A
iii)the same di-electric slab is now placed inside B, filling it completely. The two capacitors A & B are then connected as shown in figure (c). Calculate the energy stored in the system.
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68.Two square metal plates of 1 m side are kept 01 m apart, like a parallel plate capacitor, in air in such a way that one of their edges is perpendicular, to an oil surface in a tank filled with an insulating oil. The plates are connected to a battery of e.m.f. 500 volt . The plates are then lowered vertically into the oil at a speed of 0.001 m/s. Calculate the current drawn from the battery during the process, [di-electric constant of oil = 11, E0 = 8.85 x 10-12 C2/N1 m1] [JEE ’94, 6]
Ans.As here battery remains attached to the circuit V=constant. Now as due to lowering of plates in the oil, capacity will increase gradually and as q=CV the charge on capacitor will increase. This gradual increase in q results in current drawn from the battery.If at any instant, y length of plate is dipped in oil, the system will be equivalent to two capacitors in parallel, one with air and the other with oil as dielectric so that
69.The capacitance of a parallel plate capcitor with plate area ‘A’ & separation d is C. The space between the plates is filled with two wedges of di-electric constants. Kt & K2 Find the capacitance of the resulting capacitor. [JEE’96,2]
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70.Two isolated metallic solid spheres of radii R and 2R are charged such that both of these have same charge density a . The spheres are located far away from each other, and connected by a thin conducting wire. Find the new charge density on the bigger sphere. [1996-3 marks]
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71.Two capacitors A and B with capacities 3 mF and 2 mF are charged to a potential difference of 100 V and 180 V respectively. The plates of the capacitors are connected as shown in the figure with one wire from each capacitor free. The upper plate of A is positive and that of B is negative. An uncharged 2 mF capacitor C with lead wires falls on the free ends to complete the circuit. Calculate [ JEE ’97 -5 marks]
i)the final charge on the three capacitors and
ii)The amount of electrostatic energy stored in the system before and after the completion of the circuit.
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72.A conducting sphere S1 of radius r is attached to an insulating handle . Another conducting sphere S2 of radius R is mounted on an insulating stand. S2 is initially uncharged . S1 is given a charge Q, brought into contact with S2 & removed, S1 is recharged such that the charge on it is again Q & it is again brought into contact with S2 & removed. This procedure is repeated n times.[1998-8 marks]
a)Find the electrostatic energy of S2 after n such contacts with S1
b)What is the limiting value of this energy as n->infinity?
Ans.When a conducting sphere S, is brought in contact with another conducting sphere S2, a transfer of charge occurs from higher potential to lower potential till the two spheres attain equal potential. Let S1 contain charge Q before contact with S2. On contact, let a charge q shift from S1 to S2
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Ans.Let the particle be, at some instant, at a point P distant x from the origin. Of the four charges placed along y-axis, the like charges repel each other while the unlike charges attract each other. At some value of x, the attractive and repulsive forces balance each other. Therefore the attractive forces will move the charge towards origin.
75.Charges +q and -q are located at the comers of a cube of side a as shown in the figure. Find the work done to separate the charges to infinite distance. [JEE 2003-2 marks]
Ans.
Ans.(a) The free dipole, far away from the origin, travels towards origin, where a charge (+Q) is fixed. There will be a decrease in the electrostatic potential energy of the dipole. This will be equal to kinetic energy of the dipole. When the dipole is at a distance d from origin,
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78.A conducting liquid bubble of radius a and thickness t (t << a) is charged to potential V. If the bubble collapses to a droplet, find the potential on the droplet. [2005-2 marks]
Ans.A liquid-bubble contains air inside and liquid in the outside surface. When the bubble collapses into a droplet, the volume of liquid remains same in the transformation.
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True / False type
81.The work done in carrying a point charge from one point to another in an electrostatic field depends on the path along which the point charge is carried. [1981-2 marks]
Ans. False. Electrostatic force is conservative in nature. Work done in carrying a charge between two points does not depend upon path’ along which the charge is carried.The statement is false.
82.Two identical metallic spheres of exactly equal masses are taken. One is given a positive charge Q coulomb and the other an equal
Ans.True.The metallic sphere which acquires positive charges loses electrons and so it loses mass. The metallic sphere which gains negative chage gains electrons and so it gains mass. Their masses on charging are evidently different.The statement is true.
83.A small metal ball is suspended in a uniform electric field with the help of an insulated thread. If high energy X-ray beam falls on the ball, the ball will be deflected in the direction of the field.[1983-2 marks]
Ans.True.When a high energy X-ray beam falls on a metal ball, it ejects electrons from the ball. The ball therefore becomes positively charged and gets deflected in the direction of electric field.The statement is true.
84.Two protons A and B are placed in between the two plates of a parallel plate capacitor charged to a potential difference V as shown in the figure. The forces on the two protons are identical.[1986-3 marks]
Ans.True.When a parallel plate capacitor is charged to a potential difference V, a uniform electric field E-V / Jis produced between the plates. Let each of the proton, A and B, carry charge q.Force on a proton, A or B=qE Since q and E are same for each proton, the forces on them are identical.The statement is true
85.A ring of radius R carries a uniformly distributed charge +Q. A point charge -q is placed on the axis of the ring at a distance 2R from the centre of the ring and released from rest. The particle executes a simple harmonic motion along the axis of the ring. [1988-2 marks]
Ans.
The force is not proportional to displacement. The charge particle will not execute simple harmonic motion.The statement is false.Note : If x<< R, the charged particle will execute simple harmonic motion.
86.An electric line of force in the x-y plane is given by the equation x2 + y2 = 1. A particle with unit positive charge, initially at rest at the point x = l,y = 0 in the x-y plane, will move along the circular line of force. [1988-2 marks]
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A unit positive charge is placed at A(1,0).Line of force is circular with radius =1.A line of force represents the path in an electric field along which a unit positive charge moves. The unit positive charge at A is already on the circular line of force. It will move along the circular line of force.The statement is true.
Fill in the blanks type
87.Five identical capacitor plates, each of area A, are arranged such that adjacent plates are at a distance d apart. The plates are connected to a source of emf V as shown in the figure.The charge on plate 1 is ……………. and on plate 4 is [1984-2 marks]
Ans.Plates 1 and 2 form a parallel plate condenser. Plate 1 is connected to +ve terminal while plate 2 is connected to negative terminal.
88.Figure shows line of constant potential in a region in w’hich an electric field is present. The values of the potential are written in brackets Of the points A,B and C, the magnitude of the electric field is greatest at the point………[1984-2marks]
Ans.The magnitude of electric field is greatest at the point where the lines of force are crowded most, being close to each other. At B, the separation between 10V and 20 V lines is the least, as is clear from the figure.Hence the electric field is greatest at B.
89.Two small balls having equal positive charge Q (coulomb) on each are suspended by two insulating strings of equal length L(metre) from a hook fixed to a stand. The whole setup is taken in a satellite into space where there is no gravity (state of weightlessness). The angle between the two strings is ………….. and the tension in each string is……… ….newton.[1986-2 marks]
Ans.The two balls hang in gravity-free space in state of weightlessness in the satellite. There is only electrostatic force of repulsion between them. The balls will be repelled till the two strings are at 180°. The tension in each string will be equal to the electrostatic force between charges.
90.Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected and the region beween the plates of the capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes…………………[1989-2 marks]
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91.A point charge q moves from point P to point S along the path PQRS (figure) in a uniform electric field E pointing parallel to the positive direction of the X-axis. The coordinates P,Q,R and S are (a,b,0), (2a,0,0), (a,b,0) and (0,0,0) respectively. The work done by the field in the above process is given by the expression [1989-2 marks]
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92.The electric potential V at any point x,y,z (all in metre) in space is given by V = 4x2 volt. The electric field at the point (lm, 0, 2m) is………………. V/m [1992-1 mark]
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93.Five point charges, each of value +q coulomb, are placed on five vertices of a regular hexagon of side L metre. The magnitude of the force on the point charge of value -q coulomb placed at the centre of the hexagon is …. newton [1992-1 mark]
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JEE Main Home Maths Physics Chemistry
The post JEE Main Previous Year Papers Questions With Solutions Physics Electrostatics appeared first on Learn CBSE.
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JEE Main Home Maths Physics Chemistry
The post JEE Main Previous Year Papers Questions With Solutions Maths Statistics and Probatility appeared first on Learn CBSE.
Multlple Choice with ONE correct answer
1.In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. What are the dimensions of Y in MKSQ system ? [1995-2 marks]
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4.A cube has a side of length 2 x 10-2m. Calculate its volume. [2003-2 marks]
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6.A wire of length 1 = 6±0.06 cm and radius r = 0.5 ± 0.005 cm and mass m = 0.3 ± 0.003 g . Maximum percentage error in density is [2004-2 marks]
a) 4 b) 2 c) 1 d) 6.8
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7.Which of the following sets have different dimensions ? [2005-2 marks]
a)Pressure, Young’s modulus, stress
b)Emf, potential difference, electric potential
c)Heat, work done, energy
d)Dipole moment, electric flux, electric field
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8.The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentange error in the density is
a) 0.9% b) 2.4% c) 3.1% d) 4.2%
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Multiple Choice with ONE or More Than ONE correct answers
9.If L,C,R represent inductance, capacitance and resistance respectively, the combinations having dimensions of frequency are [1984-2 marks]
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10.Which of the following combinations have the dimensions of time ? L,C,R represent inductance, capacitance and resistance respectively [1986-2 marks]
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11.The dimensions of the quantities in one (or more) of the following pairs are the same. Identify the pair(s) [1986-2 marks]
a) Torque and work b) Angular momentum and work
c) Energy and Young’s modulus d) Light year and wavelength
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13.The pairs of physical quantities that have the same dimensions in (are) [1995-2 marks]
a)Reynolds number and coefficient of friction
b)Curie and frequency of a light wave
c)Latent heat and gravitational potential
d)Planck’s constant and torque
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15.The ST unit of inductance, the henry can be written as [1998-2 marks]
a)weber/ampere b) volt-sec/amp
c) joule/(ampere)2 d) ohm-second
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Matching Type
16.Match the physical quantities given in Column 1 with dimensions expressed in terms of mass (M), length (L), time (T), and charge (Q) given in Column II
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17.Column-I gives three physical quantities. Select the appropriate units for the choices given in Column-II. Some of the physical quantities may have more than one choice correct [1990-3 marks]
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18.Some physical quantities are given in column I and some possible SI units in which these quantities may be expressed are given in Coulmn II. Match the physical quantities in column I with the units in Column II…………………….. [2007-6 marks]
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Subjective / Numerical integer type
19.Give the MKS units for each of the following quantities : [1980-3 marks]
i) Young’s modulus ii) Magnetic induction iii) Power of a lens
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20.A gas bubble, from an explosion under water,oscillates with a period T proportional to padbEc • Where P is the static pressure, d is the density of water and E is the total energy of the explosion. Find the values of a,b and c [1981-3 marks]
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21.Write the dimensions of the following in terms of mass, time, length and charge
i) magnetic flux ii) rigidity modulus [1982-2 marks]
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Fill in the blanks
22.Planck’s constant has dimensions………………. [1985-2 marks]
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23.In the formula X = 3YZ2,X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are………………………[1988-2 marks]
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24.The dimensions of electrical conductivity is………………….. [1997-1 mark]
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JEE Main Home Maths Physics Chemistry
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