A uniform chain of mass $m$ and length $L$ is originally placed mid-way on the top of a fixed smooth double-sided wedge (Figure- $A$). The length of each side of the wedge is $L$ . It is then given a slight push. The kinetic energy of the chain when the whole chain has just slid to the left side of the wedge (Figure- $B$), is :

A body of $0.5 \,kg$ moves along the positive $X$-axis under the influence of a varying force $F$ (in newton) as shown below.If the speed of the object at $x=4 \;m$ is $3.16 \,ms ^{-1}$, then its speed at $x=8 \,m$ is ................. $\,ms ^{-1}$

The position $x$ of a particle moving along $x$-axis at time $(t)$ is given by the equation $t=\sqrt{x}+2$, where $x$ is in metres and $t$ in seconds. the work done by the force in first four seconds is .............. $J$

Two monkeys with the same mass stand on a branch at height $h$ above the horizontal jungle floor. Monkey $A$ steps off the branch holding the end of an inextensible rope of length $L$ whose other end is tied to another branch at height $H$, lets go at the bottom of the swing, and falls freely to the floor, as shown below. Monkey $B$ steps off and falls straight downward. Then, neglecting air resistance but not the tension in the rope, the total work $W$ done on each monkey and the speed $v$ with which each hits the floor are as follows:

Consider the collision depicted in Figure to be between two billiard balls with equal masses $m_{1}=m_{2}$ The first ball is called the cue while the second ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle $\theta_{2}=37^{\circ} .$ Assume that the collision is elastic and that friction and rotational motion are not important. Obtain $\theta_{1}$

A body of mass $0.5\; kg$ travels in a stratght line with velocity $v=a x^{3 / 2}$ where $a=5\; m ^{-1 / 2} s ^{-1}$ What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m ?$