A body of mass $2\, kg$ is thrown up vertically with K.E. of $490$  joules. If the acceleration due to gravity is $9.8$$m/{s^2}$, then the height at which the K.E. of the body becomes half its original value is given by ............ $\mathrm{m}$

If the momentum of a body is increased by $100\%$, then the percentage increase in the kinetic energy is ............ $\%$

The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as $k = a{s^2}$ where $a$ is a constant. The force acting on the particle is

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

Two bodies of masses $m$ and $4 \,m$ are moving with equal $K.E.$ The ratio of their linear momentums is

Two bodies of masses $2m$ and $m$ have their K.E. in the ratio $8 : 1$, then their ratio of momenta is