A man of \(50~\text{kg}\) mass is standing in a gravity-free space at a height of \(10~\text m\) above the floor. He throws a stone of \(0.5~\text{kg}\) 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.	\(9.9~\text m\)	2.	\(10.1~\text m\)
3.	\(10~\text m\)	4.	\(20~\text m\)

From a circular disc of radius R and mass 9M, a small disc of mass M and radius $\frac{\mathrm{R}}{3}$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc about an axis perpendicular to the plane of the disc and passing through its centre is -

(a) $\frac{40}{9}M{R}^2$                                        (b) $M{R}^2$

(c) $4\mathit{ }M{R}^2$                                           (d) $\frac{4}{9}M{R}^2$

The solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on a inclined plane. Both roll down without slipping. Which one will reach the bottom first ?

(1) Both together only when angle of inclination of plane is $45°$

(2) Both together

(3) Hollow cylinder

(4) Solid cylinder 

If $\overrightarrow{\mathrm{F}}$ is the force acting on a particle having position vector $\overrightarrow{\mathrm{r}}$ and $\overrightarrow{\mathrm{\tau }}$ be the torque of this force about the origin, then 

(a) $\overrightarrow{\mathrm{r}}.\overrightarrow{\mathrm{\tau }}\ne 0 \mathrm{and} \overrightarrow{\mathrm{F}}.\overrightarrow{\mathrm{\tau }}=0$                  

(b) $\overrightarrow{\mathrm{r}}.\overrightarrow{\mathrm{\tau }}>0 \mathrm{and} \overrightarrow{\mathrm{F}}.\overrightarrow{\mathrm{\tau }}<0$

(c) $\overrightarrow{\mathrm{r}}.\overrightarrow{\mathrm{\tau }}=0 \mathrm{and} \overrightarrow{\mathrm{F}}.\overrightarrow{\mathrm{\tau }}=0$

(d) $\overrightarrow{\mathrm{r}}.\overrightarrow{\mathrm{\tau }}=0 \mathrm{and} \overrightarrow{\mathrm{F}}.\overrightarrow{\mathrm{\tau }}\ne 0$

Two bodies of mass 1kg and 3kg have position vectors $\hat{i}+2\hat{j}+\hat{k}$ and $-3\hat{i}-2\hat{j}+\hat{k}$, respectively. The centre of mass of this system has a position vector -

(1) $-2\hat{i}+2\hat{k}$

(2) $-2\hat{i}-\hat{j}+\hat{k}$

(3) $2\hat{i}-\hat{j}-2\hat{k}$

(4) $-\hat{i}+\hat{j}+\hat{k}$

Four identical thin rods each of mass M and length t, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is 

(1) $\frac{4}{3}M{t}^2$                                   

(2) $\frac{2}{3}M{t}^2$

(3) $\frac{13}{3}M{t}^2$                                 

(4) $\frac{1}{3}M{t}^2$

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

1. Angular velocity 

2. Moment of inertia

3. Angular momentum 

4. Rotational kinetic energy

The bricks, each of length L and mass M, are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is :

(1) L/4

(2) L/2

(3) (3/2) L

(4) (11/12) L

A uniform disk of mass M and radius R is mounted on a fixed horizontal axis. A block of mass m hangs from a massless string that is wrapped around the rim of the disk. The magnitude of the acceleration of the falling block (m) is :

(1) $\frac{2M}{M+2m}g$

(2) $\frac{2m}{M+2m}g$

(3) $\frac{M+2m}{2M}g$

(4) $\frac{2M+m}{2M}g$

A horizontal force F is applied such that the block remains stationary. Then which of the following statement is false?

(1) f = mg [where f is the friction force]

(2) F = N [where N is the normal force]

(3) F will not produce torque

(4) N will not produce torque