The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height $h$ above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2.0\  s$, the tension in the string when the bob passes through $O$ is

A cane filled with water is revolved in a vertical circle of radius $4 $ meter and the water just does not fall down. The time period of revolution will be …….. $\sec$

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 particle of mass $200 \,g$, is whirled into a vertical circle of radius $80 \,cm$ using a massless string. The speed of the particle when the string makes an angle of $60^{\circ}$ with the vertical line is $1.5 \,ms ^{-1}$. The tension in the string at this position is ……….. $N$

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 ……… $rad\,s^{-1}$