On the application of an impulsive force, a sphere of mass \(500\) g starts moving with an acceleration of \(10\) m/s². The force acts on it for \(0.5\) s. The gain in the momentum of the sphere will be:

1. \(2.5\) kg-m/s

2. \(5\) kg-m/s

3. \(0.05\) kg-m/s

4. \(25\) kg-m/s

What is the acceleration of block A, if the acceleration of B is 4 $\mathrm{m}/{\mathrm{s}}^2$ towards the right at the instant shown?

                          
1. \(2.5~m/s^2\)
2. \(4~m/s^2\)
3. \(5~m/s^2\)
4. Zero

Two blocks of masses 2 kg and 3 kg placed on a horizontal surface are connected by a massless string. If 3 kg is pulled by 10 N as shown in the figure, then the force of friction acting on the 2 kg block will be: [Take g = 10 $\mathrm{m}/{\mathrm{s}}^2$]

Fundamentally, the normal force between two surfaces in contact is:

1. Electromagnetic

2. Gravitational

3. Weak nuclear force

4. Strong nuclear force

A particle of mass m is suspended from a ceiling through a massless string. The particle moves in a horizontal circle as shown in the given figure. The tension in the string is:
 

1. mg

2. 2mg

3. 3mg

4. 4mg

Choose the incorrect alternative:

The kinetic energy 'K' of a particle moving in a circular path varies with the distance covered S as K = a${\mathrm{S}}^2$, where a is constant. The angle between the tangential force and the net force acting on the particle is: (R is the radius of the circular path)

1.  ${\tan }^{-1}\left(\frac{\mathrm{S}}{\mathrm{R}}\right)$

2.  ${\tan }^{-1}\left(\frac{\mathrm{R}}{\mathrm{S}}\right)$

3.  ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{R}}\right)$

4.  ${\tan }^{-1}\left(\frac{\mathrm{R}}{\mathrm{a}}\right)$

A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then the train is:

1. moving with constant velocity.

2. in accelerated motion.

3. in retarded motion.

4. at rest.

A body of mass m is moving on a concave bridge ABC of the radius of curvature R at a speed v. The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:

1.  $\mathrm{mg}$ $-$ $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

2.  $\mathrm{mg}$ $+$ $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

3.  mg

4.  $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

The angle of banking for a cyclist taking a turn at a curve is given by tan$\mathrm{\theta } = \frac{{\mathrm{v}}^{\mathrm{n}}}{\mathrm{rg}}$ where symbols have their usual meaning. The value of n is: