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. `gsinthetasqrt((k)/(m))`
B. `(mgsintheta)/(k)`
C. `(3mgsintheta)/(k)`
D. none of these

Answer

C

Explanation

Here `omega=sqrt((k)/(3m))`, the maximum static frictional force is
`f_(max)=mumgcostheta=2tanthetamgcostheta=2mgsintheta`
Applying newton's second law on the block at lower extreme position,
`f-mgsintheta=momega^2Aimpliesf=momega^2A+mgsintheta`
As `flef_(max)`,`omega^2A=gsintheta` or `A=(3mgsintheta)/(k)`