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} $