**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) **