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ds IIT Advanced - Rotational Mechanics : Worksheet

Multiple Correct Answer Type

1. Solid sphere, ring and disc of different masses are kept on incline plane such that they start

sliding. When they reach the bottom of plane, …

(A) Time taken will be same. (B) Time taken will be different

(C) Velocities are same (D) K.E. will be same.

2. A ball moves over a fixed track as shown in the figure.

From ‘A’ to ‘B’ the ball rolls without slipping. Surface BC

is frictionless. KA, KB and KC are kinetic energies of the

ball at A, B and C, respectively. Then,

(A) hA > hC; KB > KC (B) hA > hC; KC > KA

(C) hA = hC; KB = KC (D) hA < hC; KB > KC

3. A particle moves in a circle of radius r with angular velocity . At some instant its velocity is v

and radius vector with respect to centre of the circle is r. At this particular instant centripetal

acceleration ca of the particle would be

(A) v (B) v (C) ( r) (D) v (r )

4. A thin uniform rigid rod of length is hinged at one end so that it can move

in a vertical plane by rotating about a horizontal axis through upper end. The

lower end is given a sharp blow and made to acquire a linear velocity vo.

Maximum height attained by lower end of the rod is :

(A) 2

0v

3g for vo < 6g (B)

2

03v

g for vo < 6g

(C) 2 for vo 6g (D) ofor v 3g

5. A particle of mass ‘m’ is travelling with a constant velocity v = 0ˆv i along the line

y = b, z = 0. Let dA be the area swept out by the position vector from origin to the particle in time

dt and ‘L’ the magnitude of angular momentum of particle about origin at any time ‘t’. Then

(A) L = constant (B) L constant (C) dA 2L

dt m (D)

dA L

dt 2m

6. A spherical body of radius ‘R’ rolls on a horizontal surface with

linear velocity ‘v’. Let L1 and L2 be the magnitudes of angular

momenta of the body about centre of mass and point of contact ‘P’.

Then

(A) L2 = 2L1 if radius of gyration K = R

(B) L2 = 2L1 for all cases

(C) L2 > 2L1 if radius of gyration K < R

(D) L2 > 2L1 if radius of gyration K > R

hA hC

A C

B

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7. A 2 kg mass attached to a string of length 1 m moves in a horizontal

circle as a conical pendulum. The string makes an angle = 30 with

the vertical. Select the correct alternative(s) (g = 10 m/s2)

(A) the horizontal component of angular momentum of mass about the

point of support ‘P’ is approximately 2.9 kgm2/s.

(B) the vertical component of angular momentum of mass about the

point of support ‘P’ is approximately 1.7 kgm2/s.

(C) magnitude of dL

(Ldt

= angular momentum of mass about point of support P) is

approximately 10 2

2

kg m.

s

(D) dL

dt will not hold good in this case.

Matrix-Match Type

1. In the following column I mass of each object is m and circular of radius R. Column II

represents moment of inertia.

Column I Column II

(A) Full ring (p) mR2

(B) Half ring (q)

2mR / 2

(C) Quarter ring (r) 2mR / 4

(D) Arc making an angle at the centre (s)

2mR2

2. Suppose a force F is applied at the top most point of a

rigid body of radius R and mass M.

Column I Column II

(A) Force of friction will be zero for (p) Solid sphere

(B) Force of friction will be forward for (q) Zero

(C) Force of friction will be backward for (r) Ring

(D) If a = R then force of friction (s) No body

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3. A rigid body is rolling without slipping on the horizontal surface

Column I Column II

(A) Velocity at point A i.e. VA (p) V 2

(B) Velocity at point B i.e. VB (q) Zero

(C) Velocity at point C i.e. VC (r) V

(D) Velocity at point D i.e. VD (s) 2 V

4. A circular body of mass M and radius R, initially spinning about its centre of mass with 0 is

gently placed on a rough horizontal surface. The moment of inertia of body about its C.M is

IC.M = MK2. If the coefficient of friction between the body and the surface is then :

Column I Column II

(A) Translational work done by the friction (p) ve

(B) Rotational work done by the friction (q) + ve

(C)

Larger the moment of inertia of body, the time required for rolling

motion (r) smaller

(D) Larger the moment of inertia of the body, work done by the friction (s) longer

(t) greater

5. A rigid body of mass M and radius R rolling without slipping on the inclined plane, then the

magnitude of force of friction.

Column I Column II

(A) For ring (p) Mg sin /2.5

(B) For solid sphere (q) Mg sin /3

(C) For solid cylinder (r) Mg sin /3.5

(D) For hollow sphere (s) Mg sin /2

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IIT Advanced - Rotational Mechanics : Worksheet Solutions

Multiple Correct Answer Type

1. (A), (C) 2. (A), (B) 3. (A), (C) 4. (A) , (C) , (D) 5. (A), (D)

6. (A), (C) 7. (A), (B), (C)

Matrix-Match Type

1. (A) (p); (B) (p); (C) (p); (D) (p)

2. (A) (r); (B) (p); (C) (s); (D) (q)

3. (A) (q); (B) (p); (C) (s); (D) (r)

4. (A) (q); (B) (p); (C) (s); (D) (t)

5. (A) (s); (B) (r); (C) (q); (D) (p)