Two particles each of mass `m` are connected by a light string of length `2L` as shown in the figure. A constant force `F` is applied continuoulsly at the mid`-`point of the string at right`-`angle to intial position of the string. Find the acceleration of each particle and the acceleration of approach between the particles when separation between them is `2x`

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=2TcosthetarArrT=(F)/(2costheta)`

`Tsintheta=ma_(0)`
`a_(0)=(Tsintheta)/(m)=(F)/(2m)tantheta`
`=(F)/(2m)xx(x)/(sqrt(a^(2)-x^(2)))`