Law of Conservation of Mechanical Energy

The potential energy of a $1 \mathrm{kg}$ particle free to move along the $x$-axis is given by $V\left(x\right)=\left(\frac{x^4}{4}-\frac{x^2}{2}\right) \mathrm{J}$. The total mechanical energy of the particle is $2 \mathrm{J}$. Then, the maximum speed (in $\mathrm{m} {\mathrm{s}}^{-1}$) is

In the figure shown, a particle of mass $m$ is released from the position $A$ on a smooth track. When the particle reaches at $B$, then normal reaction on it by the track is

A bomb at rest explodes into $3$ parts of the same mass. The momentum of the $2$ parts is $-2p\hat{\mathrm{i}}$ and $p\hat{\mathrm{j}}$. The momentum of the third part will have a magnitude of

Before a rubber ball bounces off from the floor, the ball is in contact with the floor for a fraction of second. Which of the following statements is correct?

An inelastic ball is dropped from a height of $100 \mathrm{m}$. Due to earth, $20\%$ of its energy is lost. To what height the ball will rise?