A particle of mass $10\, g$ moves along a circle of  radius $6.4\, cm$ with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{-4}\,J$ by the end of the second revolution after the beginning of the motion $?$ .............. $\mathrm{m} / \mathrm{s}^{2}$

Two trolleys of mass m and $3m$ are connected by a spring. They were compressed and released once, they move off in opposite direction and comes to rest after covering distances ${S_1}$and ${S_2}$ respectively. Assuming the coefficient of friction to be uniform, the ratio of distances ${S_1}:{S_2}$ is

A bullet of mass $200\,g$ having initial kinetic energy $90\,J$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40\,J$ within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is $.....m$

A body of mass $0.5\; kg$ travels in a stratght line with velocity $v=a x^{3 / 2}$ where $a=5\; m ^{-1 / 2} s ^{-1}$ What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m ?$

A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table ................ $\mathrm{J}$

A particle of mass $m $ is moving in a horizontal circle of radius $r$  under a centripetal force equal to $ - K/{r^2}$, where $K$  is a constant. The total energy of the particle is