LEVEL – I

1. The ratio of the radii of gyration of a circular disc and a circular ring of the same masses and radii about a tangential axis parallel to the their planes is

(A) √6 : √5

(B) 1 : √2

(C) √5 : √6

(D) none of these

2. A wheel of mass 2 kg having practically all the mass concentrated along the circumference of a circle of radius 20 cm, is rotating on its axis with an angular velocity of 100 rad/s. The rotational kinetic energy of the wheel is

(A) 4J

(B) 70J

(C) 400 J

(D) 800 J

3. A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in vertical position is

(A) √(2g/L)

(B) √ (3g/L)

(C) √ (g/2L)

(D) √ (g/L)

4. If a solid sphere, disc and cylinder are allowed to roll down an inclined plane from the same height

(A) cylinder will reach the bottom first

(B) disc will reach the bottom first

(C) sphere will reach the bottom first

(D) all will reach the bottom at the same time

5. A uniform solid circular cylinder of radius r is placed on a rough horizontal surface and given a linear velocity v = 2ω_{o}r and angular velocity ω_{o} as shown in the figure. The speed of cylinder when it starts rolling

(A) 5/2 ω_{o}R

(B) 3/2 ω_{o}R

(C) 5/3 ω_{o}R

(D) 2/3 ω_{o}R

6. When there is no external torque acting on a body moving in elliptical path, which of the following quantities remain constant

(A) kinetic energy

(B) potential energy

(C) linear momentum

(D) angular momentum

7. A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of this sphere

(A) total kinetic energy is conserved

(B) angular momentum of the sphere about the point of contact with the plane is conserved

(C) only the rotational kinetic energy about the centre of mass is conserved.

(D) angular momentum about the centre of mass is conserved.

8. A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω . Two objects, each of mass m are attached gently to the opposite ends of the diameter of the ring. The wheel now rotates with an angular velocity.

(A) ω M/(M + m)

(B) {(M – 2m)/(M +2m)}ω

(C) {M/(M + 2m)}ω

(D) {(M + 2m)/M} ω

9. A sphere moving at some instant with horizontal velocity v_{c} in right and angular velocity ω in anti clockwise sense. If = | v_{c} | = | ω R | . The instantaneous centre of rotation is

(A) at the bottom of the sphere

(B) at the top of the sphere

(C) at the centre of the sphere

(D) any where inside the sphere

10. A thin bar of mass M and length L is free to rotate about a fixed horizontal axis through a point at its end. The bar is brought to a horizontal position and then released. The angular velocity when it reaches the lowest point is

(A) directly proportional to its length and inversely proportional to its mass.

(B) independent of mass and inversely proportional to the square root of its length

(C) dependent only upon the acceleration due to gravity.

(D) directly proportional to its length and inversely proportional to the acceleration due to gravity.

###### ANSWER:

1. (C) 2. (C) 3. (B) 4. (C) 5. (C) 6. (D) 7. (B) 8. (C) 9. (B) 10. (B)

LEVEL – I

11 A triangular plate ABC is free to rotate about two points A and B on smooth horizontal floor. A force F is applied perpendicular to AB so as to rotate the plate about A and B separately. If α_{1} & α_{2} are the corresponding accelerations for the cases then α_{1} / α_{2} will be

(A) 1

(B) < 1

(C) > 1

(D) dependent on the force and the dimensions of the plate.

12. A uniform rod AB of mass m and length l at rest on a smooth horizontal surface. An impulse P is applied to the end B. The time taken by the rod to turn through a right angle is

(A) π ml/12P

(B) π ml/6P

(C) ml/ 6P

(D) none of these

13. A thin hollow sphere of mass m is completely filled with an ideal liquid of mass m. When the sphere rolls with a velocity v kinetic energy of the system is equal to

(A) (1/2) mv^{2}

(B) mv^{2}

(C) (4/3) mv^{2}

(D) (4/5)mv^{2}

14. A string is wrapped several times round a solid cylinder and then the end of the string is held stationary while the cylinder is released from rest with an initial motion. The acceleration of the cylinder and tension in the string will be

(A) 2g/3 and mg/3

(B) g and mg/2

(C) g/3 and mg/2

(D) g/2 and mg/3

15. A thin rod of mass m and length l is bent into a V-shaped frame at its mid point as shown in the figure. The moment of inertia of the system about an axis passing through O perpendicular to the plane of the frame is equal to

(A) Ml^{2}/12

(B) Ml^{2}/3

(C) Ml^{2}sin^{2}θ/12

(D) Ml^{2}sin^{2}θ/3

16. A cubical block of mass M and edge a slides down a rough inclined plane of inclination θ with a uniform velocity. The torque of the normal force on the block about its centre has a magnitude

(A) zero

(B) Mga

(C) Mg(a/2)sin θ

(D) Mga cos θ

17. A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the string and pulls the cylinder towards him. There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is

(A) l

(B) 2 l

(C) 3 l

(D) l

18. A uniform circular disc of radius r is placed on a rough horizontal surface and given a linear velocity v_{o} and angular velocity ω_{o} as shown. The disc comes to rest after moving some distance to the right. It follows that

(A) 3 v_{o} = 2ω_{o} r

(B) 2 v_{o} = ω_{o} r

(C) v_{o} = ω_{o}r

(D) 2 v_{o} = 3 ω_{o} r

19. Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,

(A) the heavier sphere reaches the bottom first

(B) the bigger sphere reaches the bottom first

(C) the two spheres reach the bottom together

(D) the information given is not sufficient to tell which sphere will reach the bottom first.

20. A rod of mass m is released on smooth horizontal surface making angle θ with horizontal. Then which of the following statement is incorrect.

(A) Acceleration of rod along vertical is less than g.

(B) Acceleration of centre of mass along horizontal is zero.

(C) Angular acceleration of rod is not constant.

(D) Momentum of the rod along vertical will remain constant.

###### ANSWER:

11. (B) 12. (A) 13. (C) 14. (A) 15. (A) 16. (C) 17. (B) 18. (B) 19. (C) 20. (D)