A block of mass m is connected to another block of mass M by a spring (massless) of spring constant k. The block are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force F starts acting on the block of mass M to pull it. Find the force of the block of mass M.

Options

A. (a) `(MF)/((m+M))`
B. (b) `(mF)/(M)`
C. (c) `((M+m)F)/(m)`
D. (d) `(mF)/((m+M))`

Answer

D

Explanation

Drawing free boy-diagrams for m & M,

we get `T=ma` and `F-T=Ma`
where T is force due to spring
`implies F-ma=Ma` or, `F=Ma+ma`
`:.` `a=(F)/(M+m)`
Now, force acting on the block of mass m is
`ma=m((F)/(M+m))=(mF)/(m+M)`