The coefficient of friction between block of mass m and `2m` is `mu=2tantheta`. There is no friction between block of mass 2 m and inclined plane. The maximum amplitude of the two block system for which there is no relative motion between both the blocks is

Options

A. `g sin theta sqrt(k/m)`
B. `m g sin theta/k`
C. `3m g sin theta/k`
D. None of these

Answer

C

Explanation

The maximum static frictional force is
`f=mu mg costheta=2 tan theta mg cos theta=2mg sintheta`
Applying Newton’s second law to block at lower extreme position
`f-mgsintheta=momega^(2)A Rightarrow f=momega^(2)A+mgsintheta` or ` omega^(2)A=sintheta` or `A=(3mgsintheta)/(k)` `(asomega^(2)=(k)/(3m))`