A weightless thread can bear a tension upto $3.7\,kg-wt$ . A stone of mass $500\,g$ is tied to it and revolved in a circular path of radius $4\,m$ in a vertical plane. If $g = 10\,ms^{-2}$, then the maximum angular velocity of the stone will be ……… $rad\,s^{-1}$

A pendulum of length $2 \; m$ consists of a wooden bob of mass $50 \; g$. A bullet of mass $75 \; g$ is fired towards the stationary bob with a speed $v$. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is $\dots \; ms ^{-1}$. (if $g =10 \; m / s ^{2}$ )

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 bucket tied at the end of a $1.6\, m$ long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position …….. $m/sec$ (Take $g = 10\,m/{\sec ^2}$)