A stone of mass $1\, kg$ tied to a light inextensible string of length $L = \frac{{10}}{3}m$ is whirling in a circular path of radius $L$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is $4$ and if $g$ is taken to be $10m/{\sec ^2}$, the speed of the stone at the highest point of the circle is ……. $m/\sec$

A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is $3$ times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical ……… $^o$.

A cage revolves around a vertical circle of radius $R$ with constant linear speed $\sqrt {gR}$ . The cage is connected to the revolving arm in such a manner that a boy of mass $m$ remains always vertical while standing on a weighing machine kept inside the cage. It is found that

A bob of mass $10$ $M$ is suspended through an inextensible string of length $l$. When the bob is at rest at the equilibrium position, two particles of mass $m$ each moving with velocity $u$ making an angle $60^o $ with the string strike and get simultaneously attached to the bob. What is the value of impulsive tension $(l)$ in the string during the impact ?

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$, the force it applies on the wire is