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

The potential energy of a particle in a force field is $U=\frac{A}{r^2}-\frac{B}{r},$where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is 

(1) B/2A                                     

(2)2A/B

(3)A/B                                       

(4)B/A

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