An insect is crawling in a hemi-spherical bowl of radius $R$. If the coefficient of friction between the insect and bowl is $\mu$, then the maximum height to which the insect can crawl the bowl is

Two objects having masses $1: 4$ ratio are at rest. When both of them are subjected to same force separately, they achieved same kinetic energy during times $t_1$ and $t_2$ respectively. Then, ratio of $\frac{t_2}{t_1}$ is

A block of mass 18.5 kg kept on a smooth horizontal surface is pulled by a rope of 3 m length by a horizontal force of 40 N applied to the other end of the rope. If the linear density of the rope is $0.5 \mathrm{kgm}^{-1}$ and initially the block is at rest, the time in which the block moves a distance of 9 m is

A block of mass 1.5 kg kept on a rough horizontal surface is given a horizontal velocity of $10 \mathrm{~ms}^{-1}$. If the block comes to rest after travelling a distance of 12.5 m , the coefficient of kinetic friction between the surface and the block is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )