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 stationary particle explodes into two particles of masses $x$ and $y$, which move in opposite directions with velocity $v_1$ and $v_2$. The ratio of their kinetic energies $\left(E_1: E_2\right)$ is

A bullet of mass $50 \mathrm{~g}$ is fired with a speed $100 \mathrm{~m} / \mathrm{s}$ on a plywood and emerges with $40 \mathrm{~m} / \mathrm{s}$. The percentage loss of kinetic energy is :

A ball of mass $2\,kg$ and another of mass $4\,kg$ are dropped together from a $60$ feet tall building. After a fall of $30$ feet each towards earth, their respective kinetic energies will be in the ratio of

The force $\vec F\, = F\hat i$ on a particle of mass $2\, kg$, moving along the $x-$ axis is given in the figure as a function of its position $x$. The particle is moving with a velocity of $5\, m/s$ along the $x-$ axis at $x\, = 0$. What is the kinetic energy of the particle at $x\,= 8\, m$ ? .................. $\mathrm{J}$

A particle of mass $'m'$ and charge $'q'$ is accelerated through a potential difference of $'V'$ volt. Its energy is