A ring and a disc with the same moment of inertia roll along a plane surface at the same speed. If ${\mathrm{E}}_{\mathrm{r}}$ be the rotational kinetic energy of the ring and ${\mathrm{E}}_{\mathrm{d}}$ be that of the disc, then:

1. ${\mathrm{E}}_{\mathrm{r}}$>${\mathrm{E}}_{\mathrm{d}}$

2. ${\mathrm{E}}_{\mathrm{r}}$<${\mathrm{E}}_{\mathrm{d}}$

3. ${\mathrm{E}}_{\mathrm{r}}$=${\mathrm{E}}_{\mathrm{d}}$

4. The relation depends upon the radii of the ring and disc

A solid sphere is rolling on a frictionless surface, as shown in the figure with a translational velocity of v m/s. If a sphere climbs up to a height h, then the value of v would be:
                 

1. $\ge \sqrt{\frac{10}{7}\mathrm{gh}}$                                                   

2. $\ge \sqrt{2\mathrm{gh}}$

3. $2\mathrm{gh}$                                                             

4. $\frac{10}{7}\mathrm{gh}$

The disc is placed on a rough horizontal surface and given only angular velocity ${\omega }_0$. The velocity of the centre of mass when it starts rolling is:

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 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 cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination ${30}^{°}$. The centre of mass of the cylinder has a speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be $[take$ $g=$ $10$ $m/s^2]\; :$

1. 2.2 m

2. 1.6 m

3. 1.2 m

4. 2.4 m

A disc rolls without slipping, climbs on a rough incline, and comes back. During the motion on the incline,

1.  Friction is downward during the upward journey.

2.  Friction is upward during the upward journey.

3.  Friction is zero.

4.  Information is insufficient to predict.

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 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.  $1$ $:$ $\sqrt{2}$ $:$ $\sqrt{2}$

The coefficient of friction between a solid cylinder and a rough inclined plane is just sufficient for the pure rolling of the cylinder. Which of the following bodies can move with pure rolling on the inclined plane?

1.  Hollow cylinder

2.  Solid sphere

3.  Hollow sphere

4.  Ring