In figure two identical particles each of mass m are tied together with an inextensible string. This is pulled …..

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

(a)  $\displaystyle \frac{\sqrt 3 F}{2m}$

(b) $\displaystyle \frac{ F}{2\sqrt 3 m}$

(c)   $\displaystyle \frac{2 F}{\sqrt3 m}$

(d) $\displaystyle \frac{\sqrt 3 F}{m}$

Ans: (b)
Sol:
$\displaystyle F = 2Tcos\theta$

And,
$\displaystyle a = \frac{Tsin\theta}{m}$

$\displaystyle a= \frac{Fsin\theta}{2cos\theta\times m}$

$\displaystyle a= \frac{F}{2\sqrt3 m}$