Adjacent figure shows the force-displacement graph of a moving body, what is the work done by this force in displacing body from $x = 0$ to $x = 35\,m$ ? ........... $\mathrm{J}$

A uniform chain of length $2\,m$ is kept on a table such that a length $60\,cm$ hangs freely from the edge of the table. The total mass of chain is $4\,kg$. The work done in pulling the entire chain on the table is ............. $\mathrm{J}$ (Take $g = 10\,m/s^2$)

A bullet of mass $m$ moving with a speed $v$ strikes a wooden block of mass $M$ and gets embedded into the block. The final speed is

State if each of the following statements is true or false. Give reasons for your answer.

$(a)$ In an elastic collision of two bodies, the momentum and energy of each body is conserved.

$(b)$ Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.

$(d)$ In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Work done in time $t$ on a body of mass $m$  which is accelerated from rest to a speed $v$  in time $t_1$  as a function of time $t$  is given by

In the figure shown the potential energy $(U)$ of a particle is plotted against its position $'x'$ from origin. The particle at