The center of mass of a system of particles does not depend upon:

1.	position of particles
2.	relative distance between particles
3.	masses of particles
4.	force acting on the particle

A particle is moving with a constant velocity along a line parallel to the positive x-axis. The magnitude of its angular momentum with respect to the origin is:

A rope is wrapped around a hollow cylinder with a mass of 3 kg and a radius of 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

1. 0.25 rad s^–2 

2. 25 rad s^–2

3. 5 m s^–2 

4. 25 m s^–2

A rigid body rotates with an angular momentum of \(L.\) If its kinetic energy is halved, the angular momentum becomes:
1. \(L\)
2. \(L/2\)
3. \(2L\)
4. \(L/\)$\sqrt{2}$

The coordinates of the centre of mass of a uniform plate of shape as shown in the figure are:

The radius of gyration of a uniform solid sphere about a tangent is:

1. $R\sqrt{\frac{2}{3}}$

2. $R\sqrt{\frac{2}{5}}$

3. $R\sqrt{\frac{5}{3}}$

4. $R\sqrt{\frac{7}{5}}$

Three identical spheres, each of mass M, are placed at the corners of a right-angle triangle with mutually perpendicular sides equal to 2m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of the centre of mass.

A uniform square plate ABCD has a mass of 10 kg. If two point masses of 5 kg each are placed at the corners C and D as shown in the adjoining figure, then the centre of mass shifts to the mid-point of:
          
1. OH

2. DH

3. OG

4. OF 

At t = 0, the positions of the two blocks are shown. There is no external force acting on the system. Find the coordinates of the center of mass of the system at t = 3 seconds:
   

The mass per unit length of a non-uniform rod of length L is given by $\mathrm{\mu }={\mathrm{\lambda x}}^2$ where $\mathrm{\lambda }$ is a constant and x is the distance from one end of the rod. The distance between the centre of mass of the rod and this end is:

1. $\frac{\mathrm{L}}{2}$

2. $\frac{\mathrm{L}}{4}$

3. $\frac{3\mathrm{L}}{4}$

4. $\frac{\mathrm{L}}{3}$