A body is falling under gravity from rest. When it loses a gravitational potential energy by $U,$ its speed increases to $v.$ The mass of the body shall be

In an elastic collision of two particles the following quantity is conserved

A neutron travelling with a velocity $v$ and $K.E.$ $E $ collides perfectly elastically head on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by neutron is

A ball of mass $m$  is dropped from a heigh $h$  on a platform fixed at the top of a vertical spring, as shown in figure. The platform is depressed by a distance $x.$  Then the spring constant is

A body of mass ${m_1}$ moving with uniform velocity of $40 \,m/s$ collides with another mass ${m_2}$ at rest and then the two together begin to move with uniform velocity of $30\, m/s$. The ratio of their masses $\frac{{{m_1}}}{{{m_2}}}$ is

The variation of force $F$ acting on a body moving along $x$-axis varies with its position $(x)$ as shown in figure The body is in stable equilibrium state at