Sample test -JEE advance 13-op-mag-mech-1 @viresh

7/30/2019 Sample test -JEE advance 13-op-mag-mech-1 @viresh

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1 / rev pt-11/ iit-jee-2008/ magnetism & mechanics( r otation)

PT-13 for AIPMT/AIEEE& IIT JEE-2008for 12++ scholars

mag +mech(rotation)( sep -2)

p q r sABCD

1-In the circuit shown initially the switch S is open and there Sexist no current any where but the left plate and the right Lplate of thecapacitor carry charges Q0 and - Q0 respectively + -The inductor has self inductance L and the capacitance is C.

There is no resistance any where in the circuit. The switch is closed at time t =0

and the charge of the capacitor first time becomes zero at time t = t0.In the following, column I, some statements related to the circuit are given andtheir responses are given in the column II . Match the items in the two columnscorrectly .The answer is to be given in the matrix by bubbling the matrix correctly.

Column I Column II(A) current in the circuit (p) vary harmonically with time period 4 t0.(B) charge on the capacitor (q) vary harmonically with time period 2t0.(C) magnetic energy in the circuit (r) first time becomes maximum at time t =t0

(D) rate of growth of the magnetic (s) would have same maximum valueenergy even if self inductance was 2 L

Linked Comprehension typeThis section contains four paragraphs. Each paragraph is followed by few

questions with multiple options for their answers. Choose the only one option

which is most correct.

P2- 4: Paragraph for the Q.Nos 2 to 4

There are two parallel and conducting long horizontal rails whose one endsare joined by a resistor o f resistance R.

Separation between the rails is d. A rodof mass m and resistance 2R, is of length d.The rod is placed touching the two rails.

A uniform magnetic field B is applied over the entire region between therails. The rod is projected with velocity v0 parallel to the rails at time t =0.

2-The velocity of the rod will

(a) remain constant (b) decreases linearly with time(c) increases linearly with time (d) decreases linearly with displacement

3- At certain time when induced current is i , the kinetic energy of the rod is E.Then dE/dt at the instant will be

(a) zero (b) i2 3R (c) - i2 3R (d) - i2 2R

4 - By the time rod has moved by x , the charge that would have flown through therod is


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(a) B x d/ R (b) B x d/(2m ) (c) B x d/(3R) (d) B x d/(3mR)

5-By the time , rod stops, total heat dissipated in the rod only is equal to(a) mv02 / 3 (b) mv02 / 2 (c) mv02 / 4 (d) mv02 / 6

P6- 8: Paragraph for the Q.Nos 6 to 8In a region uniform magnetic field B and electric field E are applied , both in

positive z- direction. A proton is projected from the origin (0,0,0) with veliocity u jat timet =0.6- The path of the proton will be(a) circle in x-y plane (b) parabolic in x -y plane

(c) helical with uniform pitch (d) helical with non uniform pitch

7- The proton touches the z- axis first time after the projection , at time t =t0.Then t0 is(a) independent of mass of the proton (b) proportional to charge of the proton

(c) independent of the magnetic field (d) independent of the electric field E

8- Work done by the resulting forces on the proton, up time t is(a) zero ( b) proportional to t & independent of B

(c) proportional to t2& independent of E (d) proportional to t2& independent of B

P8-11 : Paragraph for the Q.Nos : 8 to 11A uniformly dense cylinder of mass M, radius R and height H = 5R,is placed on a

rough horizontal floor which have friction coeffficent 0.4 with cylider.A horizontal force P is apllied at height H above the ground Plevel. The lne of action of the force P, intersects the axis

of the cylider. H

8- If P = 0.25 Mg, and the cylinder is not toppling, then (a) must be 0.25 (b)must be 0.4 (c) may be 0.7 (d) may be 1.09 -If P = 0.25 Mg and = 0.6 , the line of action of the normal reaction of theground passes from a point which is at distnace

(a) 0.5 R from the axis of the cylinder ( b) 0.75 R from the axis of the cylinder(c) zero from the axis (d) R from the axis of the cylinder


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10- If the = 0.6 and the value of P is increased , then the cylinder(a) slips before toppling (b) topples before slipping

(c) slipping and toppling begins simultaneously (d) never topples

11-If the slipping is to precede toppling, then (a) may be 0.3 (b) may be 0.7 (c) must be 0.5 (d) must be > 0.5

P12-15 : Paragraph for the Q.Nos : 12 to 15A unifromly dense solid disc of mass M is placed on a rough horizontal floor withplane of disc vertical. A mass less point charge q is pasted to the discat a point P which is at distance R/3 from the center . The disc isat rest and the point P is at same level as the center C of the disc. CNow at time t = 0, a uniform electric field E acting downward

is switch on. After that the disc started to roll without slip.Just after the time t =0, friction force on the disc towards right is f, clockwiseangular acceleration of the disc is and acceleration of center of disc is actowards right.

12- Which of the following relation is not correct?(a) f = M ac (b) qE R /3 = M R2/ 2(c) qE R /3 - fR = M ac R/2 (d) qE R /3 = 3M R2/ 2

13- The acceleration of the center of disc ac just after applying the electric field is(a) 2qE/(3M) (b) qE/(3M) (c) qE/ M (d) zero

14-If qE = 2Mg , then friction coefficient between the disc and the floor is(a) lesser or equal to 1/3 (b) greater or equal to 1/3

(c) greater or equal to 4/9 (d) greater or equal to 2/9

15- If the rolling motion of the disc is continued, the displacement of the center ofthe disc, by the time when the point P reaches at the lowest position, will be

(a) R /3 (b) R /2 (c) R /4 (d) zero

STRAIGHT OBJECTIVE TYPE

16- A uniform rod of mass 2kg and length 0.6 m, is hanging with upper endpivoted. A horizontal force of 12000 N is applied at the center of rod for 0.2

millisecond. As result of this impulsive blow, the center of rod begins to with

velocity ( in ms-1)


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(a) 1.2 ( b) zero (c) 0.3 (d) 0.6

17- From a tower of height H, a particle is projected with velocity u towards east attime t =0. The particle hits the ground at time t =t0. Angular momentum about the

towers foot situated on the ground, at any time t ( < t0 ) is L(t) .(a) L(t) has zero value just after the projection(b) L(t) remains constant(c) magnitude ofL(t) increases with time t(d) magnitude ofL(t) increases with time t18- In the previous problem, L( t0 ) i.e. the angular momentum at the time whenthe particle is hitting the ground , is

(a) independent of u (b) proportional to u2

(c) proportional to H2 (d) directed towards north

19-A square frame ABCD of side length L is made of amaterial of linear mass density .The frame is lying on a B Csmooth horizontal table. A current i is flowing in the frame.The sense of current is from A to B in the side AB. Suddenly

a uniform horizontal magnetic field is applied in direction A Dfrom A to B over the entire frame. If the frame is to start tipping over about oneedge, read following two statements:

(i) tipping will be about the edge AD

(ii) strength of magnetic field should be at least 2 g/ iThe correct statements are

(a) only(i) (b) only(ii) (c) both (i) and (ii) (d) none

20-A long straight wire carrying current in thepositive x- direction, is placed on the x- axis. PLet there be two small pieces A and B of the wireThe two pieces A and B are ofsame length butvery small. Let there be a point P on the y= axis as shown. A BThe magnetic field at P due to the elements A and B, will be in ratio

(a) 1/ PA : 1/ PB (b) 1/PA2 : 1/ PB2

(c) 1/PA3 : 1/ PB3 (d) 1/PA : 1/ PB

21-There is a long solenoid with 200 turns per meter. The self inductance of thesolenoid is 0.8 hennery per meter of its length. A co axial ring of radius R which is

much greater than the radius of the solenoid is placed around the solenoid. The

mutual inductance between the solenoid and the ring is nearly

(a) 0.004 hennery (b) 0.008 hennery (c) 0.04 hennery (d) zero

Sample test -JEE advance 13-op-mag-mech-1 @viresh

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