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 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 particle is tied to $20\,cm$ long string. It performs circular motion in vertical plane. What is the angular velocity of string when the tension in the string at the top is zero ………. $rad/sec$

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

A small sphere of mass $m$ is suspended by a light and inextensible string of length $l$ from a point $O$ fixed on a smooth inclined plane of inclination $\theta $ with the horizontal. The sphere is moving in a circle on the incline as shown. If the sphere has a velocity $u$ at the top most position $A$ . Then,