A block A of mass m is placed on a frictionless horizontal surface. Another block B of the same mass is kept on A and connected to the wall with the helpf of a spring of force constant K as shown in the figure. The coefficient of friction between the blocks A and B is `mu`. The blocks move together execting simple harmonic motion of amplitude 'a'. What is the maximum value of the fricitional force between A and B ?

Options

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

Answer

D

Explanation

Because of the compressions and extensions of the spring, A and B move together executing a linear S.H.M. The maximum acceleration of the system `=omega^(2)` a where a is the amplitude. A and B are not rigidly fixed. Hence there is a tendency for relative motion between them. There will be no relative motion between A and B or they will move together, as long as the limiting force of friction (f) between them =mass of B `xx` maximum acceleration
i.e. `f=m omega^(2)a " where " omega = sqrt((K)/(m+m))= sqrt((K)/(2m))`
`therefore f=m. (K)/(2m)xx a =(Ka)/(2)`