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 body of mass $m$ hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of ${60^°}$ with the vertical. The tension in the string at mean position is

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

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 ……… $rad\,s^{-1}$

The maximum and minimum tension in the string whirling in a circle of radius $2.5 \,m$ with constant velocity are in the ratio $5 : 3$ then its velocity is