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

Answer

C

Explanation

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