$A$ mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is

In the given figure, the block of mass $m$ is dropped from the point $A$. The expression for the kinetic energy of the block when it reaches point $B$ is ................

$A$ particle slides from the top of a smooth hemispherical surface of radius $R$ which is fixed on a horizontal surface. If it separates from the hemisphere at a height $h$ from the horizontal surface,then the speed of the particle is

$A$ smooth semicircular tube $AB$ of radius $R$ is fixed in a vertical plane and contains a heavy flexible chain of length $\pi R$. Find the velocity $v$ with which it will emerge from the open end $B$ of the tube,when slightly displaced.

Brakes stop a train in a distance $x$. If the braking force is reduced to one-fourth of its original value,what distance will the train travel before coming to a stop?

$A$ spring of force constant $k$ is fixed vertically on a table. $A$ ball of mass $m$ is dropped from a height $h$ onto the free end of the spring,causing the spring to compress by a distance $d$. What is the total work done in this process?