Two masses of $1 \,gm$ and $4 \,gm$ are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

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 …… .

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 $x\,= 8\, m$ ? ……………… $\mathrm{J}$

$A$ ball is projected vertically upwards. Air resistance  variation in $g$ may be neglected. The ball rises to its maximum height $H$ in a time $T$, the height being $h$ after a time $t$

$[1]$ The graph of kinetic energy $E_k$ of the ball against height $h$ is shown in figure $1$

$[2]$ The graph of height $h$ against time $t$ is shown in figure $2$

$[3]$ The graph of gravitational energy $E_g$ of the ball against height $h$ is shown in figure $3$

Which of $A, B, C, D, E$ shows the correct answers?

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