Question

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 $10m/se{c}^2$ , the speed of the stone at the highest point of the circle is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Since the maximum tension $T_S$ in the string moving in the vertical circle is at the bottom and minimum tension $T_T$ is at the top.

$\therefore T_S=\frac{m{v}_S^2}{L}+mg$ and $T_T=\frac{m{v}_T^2}{L}-mg$

$\therefore \frac{T_S}{T_T}$ = $\frac{\frac{m{v}_S^2}{L}+mg}{\frac{m{v}_T^2}{L}-mg}=\frac{4}{1}$ or $\frac{v_B^2+gL}{v_T^2-gL}=\frac{4}{1}$

or $v_B^2+gL=4v_T^2-4gL$ but $v_s^2=v_T^2+4gL$

$\therefore v_T^2+4gL+gL=4v_T^2-4gL\Rightarrow 3v_T^2=9gL$

$\therefore v_T^2=3\times g\times L=3\times 10\times \frac{10}{3}$ or $v_T=10m/sec$