A small smooth disc of mass $m$ and radius $r$ moving with an initial velocity ' $v$ ' along the positive $x$-axis collided with a big disc of mass $2m$ and radius $2r$ which was initially at rest with its centre at origin as shown in figure.

If the coefficient of restitution is $0$ then the velocity of the larger disc after the collision is 

A ball $A$ of mass $M$ collides elastically with another identical ball $B$ at rest as shown in the figure. Initially, velocity of the ball $A$ is $u \mathrm{m} {\mathrm{s}}^{-1}\text{.}$ After collision

The given figure shows a plot of the time-dependent force $F_{\mathrm{x}}$ acting on a particle in motion along the $x$-axis. What is the total impulse delivered by this force to the particle from time$t=0$ to $t=2 \mathrm{s}$?

A very small cube is released from edge of a fixed hemispherical frictionless bowl whose radius is $0.45 \mathrm{m}.$ Which of the following is correct (mass of bowl $=4 \mathrm{kg},$ mass of cube is $40 \mathrm{g}$).

A ball is thrown onto a rough floor with speed $u$ at angle $\theta =45°$. If it rebounds with speed $v$ at the same angle $\varphi =45°$. Find the coefficient of kinetic friction $\left(\mu \right)$ between the floor and the ball. The coefficient of restitution, $e=0.6$

Sand is falling on a flat car being pulled with constant speed. The rate of mass falling on the cart is constant. Then the horizontal component of force exerted by the falling sand on the cart,