The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is:
     
1. 24 Ns

2. 20 Ns

3. 12 Ns

4. 6 Ns

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 $m_1<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>m_2$ 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. $\theta ={\tan }^{-1}\left(\frac{1}{2}\right)to<mspace\; width="1em"></mspace>the<mspace\; width="1em"></mspace>x‐axis$

4.$\mathrm{<mspace\; width="1em"></mspace>\theta }={\tan }^{-1}\left(\frac{-1}{2}\right)to<mspace\; width="1em"></mspace>the<mspace\; width="1em"></mspace>x‐axis$

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 $2<mspace\; width="1em"></mspace>m{s}^{-1}$ 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