The potential energy of a $2 \mathrm{kg}$ 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 ${\mathrm{ms}}^{-1}$) is

The potential energy curve $U$ of a particle as a function of its position is shown. The particle has total mechanical energy $E$ of $3.0 \mathrm{J}$. Which of the following is correct?

A simple pendulum of length $L$ is suspended from the top of a flat beam of thickness $\frac{L}{2}$. The bob is pulled away from the beam so that it makes an angle $\mathrm{\theta }$ with the vertical as shown in the figure. It is then released from rest. If $\varphi$ is the maximum angular deflection to the right, then

The blocks $A$ and $B$ shown in the figure have masses $M_{\mathrm{A}}=5 \mathrm{kg}$ and $M_{\mathrm{B}}=4 \mathrm{kg}$. The system is released from rest. The speed of $B$ after $A$ has travelled a distance $1 \mathrm{m}$ along the incline is