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 coefficient 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 reaction between the blocks is

Options

A. zero only if `m_(1)=m_(2)`
B. zero in all cases
C. non - zero only if `m_(1) gt m_(2)`
D. non - zero only if `m_(1) lt m_(2)`

Answer

B

Explanation

For `a lt mu g`
`N=0`
Foa `agt mu g `
`a_(m_(1)+m_(2))=((m_(1)+m_(2))a+mu(m_(1)+m_(2))g)/((m_(1)+m_(2)))`
`=a-mug` ` w.r.t. ` platform
For `m_(1)`
`m_(1)a-mu m_(1)g+N=m_(1)xxa_(m_(1)+m_(2))`
`m_(1)a-mu m_(1)g+N=m_(1)(a- mu g )`
`N=0`