The block starts from rest as shown in the figure. Find the work done by the force of $10 \,N$ and friction in the time $0$ to $4 \,s$. [Take, $g=10 \,m/s^2$]

$A$ child swings on a swing such that the minimum and maximum heights from the ground are $0.75 \ m$ and $2 \ m$ respectively. The maximum velocity of the swing is ...... $ms^{-1}$.

Define elastic collision and inelastic collision.

Two blocks $A(5 \ kg)$ and $B(2 \ kg)$ attached to the ends of a spring of spring constant $k = 1120 \ N/m$ are placed on a smooth horizontal plane with the spring undeformed. Simultaneously,velocities of $3 \ m/s$ and $10 \ m/s$ along the line of the spring in the same direction are imparted to $A$ and $B$. Then:

$A$ particle of mass $m$ is moving along the $x$-axis with initial velocity $u \hat{i}$. It collides elastically with a particle of mass $10m$ at rest and then moves with half its initial kinetic energy (see figure). If $\sin \theta_{1} = \sqrt{n} \sin \theta_{2}$,then the value of $n$ is:

In the figure shown,two identical balls of mass $M$ and radius $R$ each are placed in contact with each other on a frictionless horizontal surface. $A$ third ball of mass $M$ and radius $R$ is coming down vertically with a velocity $v_0$. It simultaneously hits the two balls. The smaller ball (top ball) does not stop after the collision but continues to move downwards with a speed $v_0/2$. Find the speed of each bigger ball after the collision.