A man of \(50\) kg mass is standing in a gravity free space at a height of \(10\) m above the floor. He throws a stone of \(0.5\) kg mass downwards with a speed of \(2~\text{ms}^{-1}\). When the stone reaches the floor, the distance of the man above the floor will be: 

1.	\(9.9\) m	2.	\(10.1\) m
3.	\(10\) m	4.	\(20\) m

A thin wire of length L and uniform linear mass density $\rho$ is bent into a circular loop with the centre at O as shown. The moment of inertia of the loop about the axis XX' is

1. $\frac{\rho L^3}{8{\pi }^2}$
2. $\frac{\rho L^3}{16{\pi }^2}$
3. $\frac{5\rho L^3}{16{\pi }^2}$
4. $\frac{3\rho L^3}{8{\pi }^2}$

The one-quarter sector is cut from a uniform circular disc of radius R. This sector has a mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation will be: 

A billiard ball of mass m and radius r, when hit in a horizontal direction by a cue at a height h above its centre, acquires a linear velocity $v_0$ . The angular velocity ${\omega }_0$ acquired by the ball will be:

1. $\frac{5v_0{r}^2}{2h}$

2. $\frac{2v_0{r}^2}{5h}$

3. $\frac{2v_{0}h}{5r^2}$

4. $\frac{5v_{0}h}{2r^2}$

A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the path followed by its center of mass?

1.		2.
3.		4.

The moment of inertia of a uniform circular disc of radius 'R' and mass 'M' about an axis touching the disc at its diameter and normal to the disc will be:
1. $\frac{3}{2}M{R}^2$
2. $\frac{1}{2}M{R}^2$
3. $M{R}^2$
4. $\frac{2}{5}M{R}^2$

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 circular platform is mounted on a frictionless vertical axle. Its radius is R = 2m and its moment of inertia about the axle is 200 kg m². Initially, it is at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at a speed of 1 m s^–1 relative to the ground. The time taken by the man to complete one revolution is:
1. $\mathrm{\pi } \sec$                 
2. $\frac{3\mathrm{\pi }}{2}\sec$
3. $2\mathrm{\pi } \sec$               
4. $\frac{\mathrm{\pi }}{2}\sec$

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:

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