$A$ uniform chain of mass $M$ and length $L$ is placed on a frictionless table such that $1/3$ of its length is hanging over the edge. Find the work done to pull the hanging part back onto the table.

$A$ bullet of mass $1 \ kg$ fired with a speed $2 \ m \ s^{-1}$ from $x = 0$ passes through a block of wood whose centre is kept at a distance of $10 \ m$ from the origin as shown in figure. The retarding force $F_r$ on the bullet within the wooden block is $-0.5/x$. The minimum length of the block (up to $1$ decimal digit) required to completely stop the bullet is (Assume $e^4 = 55$). (in $m$)

$A$ force of $(6x^2 - 4x + 3) \text{ N}$ acts on a body of mass $0.75 \text{ kg}$ and displaces it from $x = 2 \text{ m}$ to $x = 5 \text{ m}$. The work done by the force is (in $\text{ J}$)

The graph between power $(P)$ and time $(t)$ is given below. Which of the following options is correct for the work done by the force [from $t = 0$ to time $t$]?

The work done by a force $\vec F = (-6x^3\hat i)\, N$,in displacing a particle from $x = 4\, m$ to $x = -2\, m$ is .............. $J$.

The work done by a force $\vec{F} = -5x^4 \hat{i} \text{ N}$ in displacing a body from $x = 2 \text{ m}$ to $x = -2 \text{ m}$ is: (in $\text{ J}$)