Two masses each equal to m are lying on x-axis at `(-a,0)(+a,0)` respectively as shown in figure They are connected by a light string A force F is applied at the origin along vertical direction As a result the masses move toward each other without loosing contact with ground What is the acceleration of each mass? Assume the instantanceous position of the masses as`(-x,0)`and `(x,0)`

Options

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

Answer

c

Explanation

From figure `F = 2T cos theta`
`T = F//2 cos theta`
The force responsible for motion of masses m x-axis is `T sin theta`
`ma = T sin theta = (F)/(2 sin theta) xxsin theta`
`= (F)/(2) tan theta = (F)/(2)xx(OB)/(OA) = (F)/(2) xx(x)/(sqrt((a^(2) - x^(2)))`
So `a = (F)/(2m) = (x)/(sqrt(a^(2) - x^(2))`