A uniform sphere of mass m and radius r rolls without slipping down an inclined plane,  inclined at an angle of 45° to the horizontal. The minimum value of the coefficient of friction between the sphere and the inclined plane will be:

1. 1/6

2. 2/7

3. 1/5

4. 1/7

A solid sphere is rolling without slipping such that the velocity of its centre of mass is v. Ratio of speeds  of horizontal extreme points A and B is
                             
1. 1:1

2. $\sqrt{2}$:1

3. 2:1

4. 1:$\sqrt{2}$

A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio K_t : (K_t + K_r) for the sphere will be:

1. 7:10

2. 5:7

3. 10:7

4. 2:5

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle  θ without slipping and slipping down the incline without rolling will be:
1. 5:7
2. 2:3
3. 2:5
4. 7:5

A ring and a disc have the same mass and roll without slipping at the same linear velocity v. If the total kinetic energy of the ring is 8 J, then the total kinetic energy of the disc will be:

1. 8 J

2. 6 J

3. 16 J

4. 4 J

A solid sphere slides from the top to the bottom of a smooth inclined plane. It takes time T. If it rolls on a rough inclined plane of the same dimension, then the time taken by it to reach from top to the bottom will be:

1.  $\sqrt{3}T$

2.  $\sqrt{\frac{2}{5}}T$

3.  $\sqrt{\frac{5}{3}}T$

4.  $\sqrt{\frac{7}{5}}T$

A drum of radius R and mass M rolls down without slipping along an inclined plane of angle θ. The frictional force:
1. Decreases the rotational and translational motion
2. Dissipates energy as heat
3. Decreases the rotational motion
4. Converts translational energy to rotational energy

 A disc is set in pure roll on an inclined plane. Let us take three points on the disc as shown in the figure. Then v_B : v_C : v_D equals: (v_B, v_c and v_D are corresponding speeds)

1.  $1$ $:$ $1$ $:$ $1$

2.  $1$ $:$ $2$ $:$ $\sqrt{2}$

3.  $2$ $:$ $1$ $:$ $\sqrt{2}$

4.  $1$ $:$ $\sqrt{2}$ $:$ $\sqrt{2}$

A block of mass m slides down on a smooth inclined plane and reaches the bottom with speed v. If the same mass is in the form of a ring which rolls down on an identical inclined plane, where friction is sufficient for pure rolling, the speed of the ring at the bottom will be:

1. $v$

2. $v\sqrt{2}$

3. $\frac{v}{\sqrt{2}}$

4. $v\sqrt{\frac{2}{5}}$

A disc and a solid sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

1. Sphere

2. Both reach at the same time

3. Depends on their masses

4. Disc