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. $\sqrt{3} \frac{G m}{L^{2}}$

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}+2 F^{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} G m}{L^{2}}$