Two particle 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

The string is pulled vertcally upwards with a small but constant force F . A s 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

Explanation

` :. " " F = 2T cos theta `
` rArr T = F/(2 cos theta ) " " ….(1)`
` :. ` Magnitude of acceleration of particel (a.)
`= (T sin theta)/m " " ...(2)`
[By using (1) in eqn .(2) ]
` :. " " a. = (F tan theta)/(2m) = F/(2m) x/sqrt(a^(2)-x^(2))`.