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

• A
  $\frac{F}{{2m}}\,\frac{a}{{\sqrt {{a^2} - {x^2}} }}$
• B
  $\frac{F}{{2m}}\,\frac{x}{{\sqrt {{a^2} - {x^2}} }}$
• C
  $\frac{F}{{2m}}\,\frac{x}{a}$
• D
  $\frac{F}{{2m}}\,\frac{{\sqrt {{a^2} - {x^2}} }}{x}$