Question

Three point masses of mass $m$ each are placed on the vertex of equilateral triangle of side $L$ in a gravity free region. Each point mass is given same speed $V$ in such a way that separation between them does not change, then $V$ is

• A. $\sqrt{\frac{Gm}{2L}}$
• B. $\sqrt{\frac{Gm}{L}}$
• C. $\sqrt{\frac{3Gm}{2L}}$
• D. $\sqrt{\frac{Gm}{3L}}$

Answer 1

The correct option is B $\sqrt{\frac{Gm}{L}}$


Each mass moves in a circular path of radius $\frac{L}{\sqrt{3}}$.

$F_C=2Fcos{30}^{\circ }=2\frac{G{m}^2}{L^2}\times \frac{\sqrt{3}}{2}$

$F_c=\frac{m{V}^2}{R}$

$\frac{\sqrt{3}m{V}^2}{L}=\frac{\sqrt{3}G{m}^2}{L^2}\Rightarrow V=\sqrt{\frac{Gm}{L}}$