If the potential energy of a gas molecule is $U = \frac{M}{{{r^6}}} - \frac{N}{{{r^{12}}}},M$ and $N$ being positive constants, then the potential energy at equilibrium must be
zero
$\frac {M^2}{4N}$
$\frac {N^2}{4M}$
$\frac {MN^2}{4}$
A body of mass $2\,kg$ makes an elastic collision with another body at rest and continues to move in the original direction with one fourth of its original speed, The mass of the second body which collides with the first body is ............... $\mathrm{kg}$
Two blocks $A$ and $B$ of masses $1\, kg$ and $2\, kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to strech the spring and then released. The ratio of $K.E.s$ of both the blocks is
The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is
Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $W$. Here $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$. The velocity of particle at time $t = 2\, sec$. will be ........... $\mathrm{m}/ \mathrm{s}$
When the momentum of a body increases by $100\%$, its $KE$ increases by .............. $\%$