A force $F$ acting on an object varies with distance $x$ as shown in the figure. The work done by the force in moving the object from $x = 0$ to $x = 8\,m$ is  ......... $J$

A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

If $F = 2x^2 -3x -2$, then choose correct option

After head on elastic collision between two balls  of equal masses , one is observed to have a speed of  $3\,\,m/s$  along positive  $x-$ axis and the other has a speed of  $2\,\,m/s$  along negative $x$  axis. The original velocities of the balls are

A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the bullet will be

If the potential energy of a gas molecule is $U = \frac{M}{{{r^6}}} - \frac{N}{{{r^{12}}}},M$ and $N$ being positive constants, then the potential energy at equilibrium must be