Question

In the figure, two identical particles each of mass $m$ are tied together with an inextensible massless string. This is pulled at its centre with a constant force $F$ . If the whole system lies on a smooth horizontal plane, then the acceleration of each particle towards each other at the instant shown in the figure is

• A. $\frac{\sqrt{3} \, }{2 \, }\frac{F}{m}$
• B. $\frac{1}{2 \sqrt{3}}\frac{F}{m}$
• C. $\frac{2}{\sqrt{3}}\frac{F}{m}$
• D. $\sqrt{3}\frac{F}{m}$

Answer 1

Answer: (B)

$2Tcos 30^{o}=F$
$\Rightarrow \, \, T=\frac{F}{2 cos 30^{o}}=\frac{F}{\sqrt{3}}$

$\Sigma \, F_{y}=Tcos 60^{o}=\frac{F}{2 \sqrt{3}}$
$\Sigma \, F_{y}=ma_{y}$
$\Rightarrow \, \, a_{y}=\frac{F}{2 \sqrt{3} m}$