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Two particles of mass $m$ each are tied at the ends of a light string of length $2a$ . The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $'a'$ from the centre $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$ . As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2x$ , is
$\frac{F}{{2m}}\,\frac{a}{{\sqrt {{a^2} - {x^2}} }}$
$\frac{F}{{2m}}\,\frac{x}{{\sqrt {{a^2} - {x^2}} }}$
$\frac{F}{{2m}}\,\frac{x}{a}$
$\frac{F}{{2m}}\,\frac{{\sqrt {{a^2} - {x^2}} }}{x}$
Solution
$F=2 T \cos \theta$
$\Rightarrow T=\frac{F}{2 \cos \theta}$
Magnitude of acceleratior of the particle
$=\frac{T \sin \theta}{m}$
$=\frac{F \tan \theta}{2 m}=\frac{F}{2 m} \frac{x}{\sqrt{a^{2}-x^{2}}}$
