A block P of mass m is placed on a smooth horizontal surface. A block Q of the same mass is placed over the block P and the coefficient of static friction between them is `mu`. A spring of spring constant K is attached to block Q. The blocks are displaced together to a distance A and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is:

Options

A. zero
B. KA
C. `(1)/(2)KA`
D. `mu mg`

Answer

C

Explanation

Angular frequency of system `omega=sqrt((k)/(m+n))=sqrt((k)/(2m))`
Maximum acceleration `a_(max)-omega^(2)A`
Frictional force between P and Q = force exerted on lower block = `m omega^(2)A=m((K)/(2m))A=(kA)/(2)`