Two identicle particles A and B, each of mass m, are interconnected by a spring of stiffness k. If particle B experiences a forec F and the elongation of the spring is x, the acceleration of particle B relative to particle A is equal to

Options

A. `(F)/(2m)`
B. `(F-kx)/(m)`
C. `(F-2kx)/(m)`
D. `(kx)/(m)`

Answer

C

Explanation

Equation of motion for A.
`kx=ma implies a=(kx)/(m)`
For B: `F-T=ma'`
`implies a'=(F-kx)/(m)`
Thus, relative acceleration =`a_(r ) =|a'-a|=(F-2kx)/(m)`