A sphere of mass $m$ travelling at constant speed $v$ strike another sphere of same mass. If coefficient of restitution is $e$, then ratio of velocity of both spheres just after collision is :-

- A
$\frac{1-e}{1+e}$

- B
$\frac{1+e}{1-e}$

- C
$\frac{e+1}{e-1}$

- D
$\frac{e-1}{e+1}$

A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the bullet will be

A force $F$ acting on an object varies with distance $x$ as shown in the figure. The work done by the force in moving the object from $x = 0$ to $x = 8\,m$ is ......... $J$

A particle moves with a velocity $\vec v\, = \,5\hat i - 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be ............... $\mathrm{J} / \mathrm{s}$

A body of mass $2\,kg$ makes an elastic collision with another body at rest and continues to move in the original direction with one fourth of its original speed, The mass of the second body which collides with the first body is ............... $\mathrm{kg}$

A mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is