A block P of mass m is placed on horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k, the two blocks are pulled by distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks.

Options

A. `kA//2`
B. `kA`
C. `mu_smg`
D. zero

Answer

A

Explanation

Let `omega` be the angular frequency of the system.
The maximum acceleration of the system,
`a=omega^2A=((k)/(2m))A[omega=sqrt((k)/(m+m))=sqrt((k)/(2m))]`
The force of friction provides this acceleration.
`:.` `f=ma=m((kA)/(2m))=(kA)/(2)`