In the figure shown the potential energy $(U)$ of a particle is plotted against its position $'x'$ from origin. The particle at
$x_1$ is in stable equilibrium
$x_2$ is in stable equilibrium
$x_3$ is in stable equilibrium
None of these
A mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is
A rifle bullets loses $\left(\frac{1}{20}\right)^{th}$ of its velocity in passing through a plank. Assuming that the plank exerts a constant retarding force, the least number of such planks required just to stop the bullet is .............
A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, then power delivered to the particle in time $T$ is
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
A shell is fired from a canon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces come to rest. The speed of the other piece immediately after the explosion is