A graph between kinetic energy and momentum of a particle is plotted as shown in the figure. The mass of the moving particle is ........ $kg$.

Two particles having masses $4\, g$ and $16\, g$ respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is $n : 2 .$ The value of $n$ will be ...... .

If a man increase his speed by $2 \,m/s$ , his K.E. is doubled, the original speed of the man is

A spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released the spring exerts equal and opposite forces for the same time $t$ on each toy cart. If the coefficients of friction $\mu $ between the ground and the toy carts are equal, then the displacement of the toy carts are in the ratio

A body initially at rest, breaks up into two pieces of masses $2 M$ and $3 M$ respectively, together having a total kinetic energy $E$. The piece of mass $2 M$, after breaking up, has a kinetic energy

A spring of unstretched length $l$ has a mass $m$ with one end fixed to a rigid support .Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is