The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is

A small block of mass $m$ slides along a smooth frictional track as shown in the figure. If it starts from rest at $P$ , velocity of block at point $Q$ is

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

A particle of mass $M$ is moving in a horizontal circle ofradius $R$ with uniform speed $v$. When it moves from one point to a diametrically opposite point, its
 

The force acting on a body moving along $x-$ axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at

Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2 m$ at rest the collision is head on and elastic in nature. After the collision the fraction of energy lost by colliding body $A$ is