Question

Three particles $A,B$ and $C$ each of mass $m$ are lying at the corners of an equilateral triangle of side $L$. If the particle $A$ is released keeping the particles $B$ and $C$ fixed, the magnitude of instantaneous acceleration of $A$ is

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

Answer 1

Answer: (D)

At this moment,
Forces acting on particle at $A$ can be shown,

where, $F=\frac{G{m}^2}{L^2}$

$\Rightarrow$ Net force will be resultant of both,
$F_{\text{resultant }}=\sqrt{F^2+F^2+2F^2\cos 60^{\circ }}=\sqrt{3}F$
$\Rightarrow F_{\text{resultant }}=\frac{\sqrt{3}G{m}^2}{L^2}$
$a=\frac{F}{m}=\frac{\sqrt{3}Gm}{L^2}$