Two blocks of masses 5 kg and 3 kg are placed in contact over an inclined surface of angle `37^(@)`, as shown. `mu_(1)` is friction coefficient between 5 kg block and the surface of the incline and similarly, `mu_(2)` is friction coefficient betweem the 3 kg block and the surface of the incline. After the release of the blocks from the inclined surface.

Options

A. if `mu_(1)=0.5` and `mu_(2)=0.3` then `5kg` block exerts `3N` force on the `3kg` block
B. if `mu_(1)=0.5` and `mu_(2)=0.3` then `5kg` block exters `8N` force on the `3kg` block
C. if `mu_(1)=0.3` and `mu_(2)=0.5` then `5kg` block exerts `1N` force on the `3kg` block.
D. if `mu_(1)=0.3` and `mu_(2)=0.5` then `5 kg` block exerts no force on the `3kg` block.

Answer

A, D

Explanation

Case `-I: mu_(1)=0.5,mu_(2)=0.3`
Along the incline, acceleration of `5kg` block will be less than acceleration of `3kg` block provided they move along on the incline. The reason is greater frictino coefficient of `5kg` block, as acceleration along the incline is `g sin theta - mu g cos theta `One to the contain, both blocks will move together. In this case `FBDs` of both are shown.

For `5kg` block
`m_(1)g sin theta +N -mu_(1)m_(1)g cos theta =m_(1)a`
For `3kg` block
`m_(2)g sin theta-N-mu_(2)m_(2)g cos theta m_(2)a`