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A body falls on a surface of coefficient of restitution 0.6 from a height of 1 m. Then the body rebounds to a height of 
(1) 0.6 m
(2) 0.4 m
(3) 1 m
(4) 0.36 m

A ²³⁸U nucleus decays by emitting an alpha particle of speed v ms^–1. The recoil speed of the residual nucleus is (in ms^–1) 
(1) –4v/234
(2) v/4
(3) –4v/238
(4) 4v/238

A cannon ball is fired with a velocity 200 m/sec at an angle of 60° with the horizontal. At the highest point of its flight ,it explodes into 3 equal fragments, one going vertically upwards with a velocity 100 m/sec, the second one falling vertically downwards with a velocity 100 m/sec. The third fragment will be moving with a velocity 
(1) 100 m/s in the horizontal direction
(2) 300 m/s in the horizontal direction
(3) 300 m/s in a direction making an angle of 60° with the horizontal
(4) 200 m/s in a direction making an angle of 60° with the horizontal

Two blocks having equal masses stick together after the collision. If their combined velocity after the collision is equal to the arithmetic mean velocity of them before the collision, then the coefficient of restitution is:
(1)  Zero
(2)  0.5
(3)  0.8
(4)  1

A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to mass of 3m moving vertically upward (along the y-axis) with velocity 2v. The final velocity of the combination is
(a) $\frac{1}{4}\mathrm{v}\hat{\mathbf{i}}+\frac{3}{2}\mathrm{v}\hat{\mathbf{j}}$                                   
(b) $\frac{1}{3}\mathrm{v}\hat{\mathbf{i}}+\frac{2}{3}\mathrm{v}\hat{\mathbf{j}}$
(c) $\frac{2}{3}\mathrm{v}\hat{\mathbf{i}}+\frac{1}{3}\mathrm{v}\hat{\mathbf{j}}$                                   
(d) $\frac{3}{2}\mathrm{v}\hat{\mathbf{i}}+\frac{1}{4}\mathrm{v}\hat{\mathbf{j}}$

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 

Two identical balls \(\mathrm{A}\) and \(\mathrm{B}\) having velocities of \(0.5~\text{m/s}\) and \(-0.3~\text{m/s}\) respectively collide elastically in one dimension. The velocities of \(\mathrm{B}\) and \(\mathrm{A}\) after the collision respectively will be:
1. \(-0.5 ~\text{m/s}~\text{and}~0.3~\text{m/s}\) 
2. \(0.5 ~\text{m/s}~\text{and}~-0.3~\text{m/s}\)
3. \(-0.3 ~\text{m/s}~\text{and}~0.5~\text{m/s}\)
4. \(0.3 ~\text{m/s}~\text{and}~0.5~\text{m/s}\)

A particle of mass m moving with velocity v strikes a stationary particle of mass 2m and sticks to it. The speed of the system will be 
(1) v/2
(2) 2v
(3) v/3
(4) 3v