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 center 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 :

Options

A. `(F)/( 2m) (a)/( sqrt(a^(2) -x^(2)))`
B. `(F)/( 2m) (x)/( sqrt( a^(2) -x^(2)))`
C. `(F)/( 2m ) ( x )/( a)`
D. `( F)/(2m) ( sqrt( a^(2) -x^(2)))/(x)`

Answer

B