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Two particles of mass m each are tied at...

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 :

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`

Text Solution

Verified by Experts

The correct Answer is:
B
`F = 2T cos theta rArr T = F/(2 cos theta)`
Magnitude of acceleration of the particle.
`a = (T sin theta)/m = (F tan theta)/(2m)`
`= F/(2m) x/sqrt(a^(2) - x^(2))`
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