Two blocks of masses `m_(1)` and `m_(2)` are placed in contact with each other on a horizontal platform as shown in figure The coefficent of friction between `m_(1)` and platform is `2mu` and that between block `m_(2)` and platform is `mu`.The platform moves with an acceleration `a` . The normal reation between the blocks is

Options

A. zero in all cases
B. zero only if `m_(1) = m_(2)`
C. non zero only if `a gt2 mu g`
D. non zero only if `a gt mu g`

Answer

D

Explanation

Maximum friction available to `m_(2)` is
`(f_(max)) = mu m_(2)g`
Therefore maximum acceleration which can be provided to `m_(2)` by friction (without the help of normal reaction from `m_(1)`) is
`a_(max) = (f_(max))/(m_(2)) = mu g`
If `a gt mu g`. normal reation from `m_(1)(on m_(2))` is non zero