A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t^{\prime}$ is proportional to :
$t^{\frac{1}{4}}$
$t^{\frac{3}{4}}$
$t^{\frac{3}{2}}$
$t^{\frac{1}{2}}$
A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............
Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on horizontal portion $MN$. The ratio of the heights attained by $A$ and $B$ after collision will be (neglect friction)
A force $\vec F = (5\hat i + 3\hat j)\;N$is applied over a particle which displaces it from its original position to the point $\vec s = (2\hat i - 1\hat j)$m. The work done on the particle is.........$J$
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
A uniform chain of length $2\,m$ is kept on a table such that a length $60\,cm$ hangs freely from the edge of the table. The total mass of chain is $4\,kg$. The work done in pulling the entire chain on the table is ............. $\mathrm{J}$ (Take $g = 10\,m/s^2$)