A frictionless track $ABCDE$ ends in a circular loop of radius $R$ .A body slides down the track from point $A$ which is at a height $h = 5\, cm$. Maximum value of $R$ for the body to successfully complete the loop is .................. $\mathrm{cm}$

A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ $meter$ as shown in figure. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ............. $\mathrm{m}/ \mathrm{s}$

A body of mass $1\, kg$ is thrown upwards with a velocity $20\, m/s$. It momentarily comes to rest after attaining a height of $18\, m$. How much energy is lost due to air friction ............. $\mathrm{J}$  $(g = 10\, m/s^2)$

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 force $\overrightarrow F = (5\hat i + 3\hat j)$Newton is applied over a particle which displaces it from its origin to the point $\overrightarrow r = (2\hat i - 1\hat j)$ metres. The work done on the particle is..............$J$

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