A body of mass \((4m)\) is lying in \(xy\text-\)plane at rest. It suddenly explodes into three pieces. Two pieces each of mass \((m)\) move perpendicular to each other with equal speeds \((v)\). The total kinetic energy generated due to the explosion is:
1. \(mv^2\)
2. \(\frac{3}{2}mv^2\)
3. \(2mv^2\)
4. \(4mv^2\)

A uniform force of (3i + j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2i+k) m to position (4i+3j-k) m. The work done by the force on the particle is-

(1) 9J

(2) 6J

(3) 13J

(4) 15J

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms^-1 and the second part of mass 2kg moves with 8 ms^-1 speed. If the third part flies off with 4 ms^-1 speed, then its mass is

(1) 3kg
 

(2) 5kg
 

(3) 7kg
 

(4) 17kg

Two spheres A and B of masses $m_1 and m_2$ respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction.The mass A moves after collision in the direction

(1)same as that of B

(2)opposite to that of B

(3)$\theta ={\tan }^{-1}\left(\frac{1}{2}\right)to the x‐axis$

(4)$\theta ={\tan }^{-1}\left(\frac{-1}{2}\right)to the x‐axis$

The potential energy of a system increases if work is done

(1) by the system against a conservative force 

(2) by the system against a nonconservative force

(3) upon the system by a conservative force

(4) upon the system by a nonconservative force

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is

(a) 21 J                                                  (b) 26 J

(c) 13 J                                                   (d) 18 J

A ball moving with velocity $2 m{s}^{-1}$ collides head on with another stationery ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in $m{s}^{-1}$) after collision will be 

(1)0,1                                               

(2)1,1

(3)1,0.5                                             

(4)0,2 

An engine pumps water through a hosepipe. Water passes through the pipe and leaves it with a velocity of 2 $m{s}^{-1}.$The mass per unit length of water in the pipe is 100 $kg{m}^{-1}.$What is the power of the engine?

1. 400 W                                       

2. 200 W

3. 100 W                                       

4. 800 W

A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, the power delivered to the particle is 

(1) $\frac{{\mathrm{Mv}}^2}{\mathrm{T}}$                                 

(2) $\frac{1}{2}\frac{{\mathrm{Mv}}^2}{{\mathrm{T}}^2}$

(3) $\frac{{\mathrm{Mv}}^2}{{\mathrm{T}}^2}$                                   

(4) $\frac{1}{2}\frac{{\mathrm{Mv}}^2}{\mathrm{T}}$