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`

Explanation

When the separation between particles is `2x`
Point `C:`

`2Tcostheta=F`
`T=(F)/(2costheta)`
Particle`:`

`Tsintheta=ma`
`(F)/(2costheta)sintheta=ma`
Acceleration of particle
`a=(F)/(2m)tantheta=(F)/(2m)xx(x)/(sqrt(L^(2)-x^(2)`
Acceleration of approach `h=a+a=2a`
`=(F)/(m)xx(x)/(sqrt(L^(2)-x^(2)))`