Two blocks `A` and `B` of same masses are resting in equilibrium on an inclined plane having inclination with horizontal `=alpha(gt0)`. The blocks are touching and exerting no zero normal force on each other with block `B` higher than `A`. Coeffcient of static friction of `A` with incline `=1.2` adn of `B=0.8`. If motons not imminent

Options

A. `alphagt30^(@)`
B. `("Friction")_(A)gt("Friction")_(B)`
C. `alphagt45^(@)`
D. `("Friction")_(A)=("Friction")_(B)`

Answer

B, C

Explanation

`2m sinalpha lt 2mg cos alpha`
`f_(A)=mg sin alpha +N`
`f_(B)=mg sin alpha-N`
To show `N!=0`
`f_(b_("max"))=0.8mgcosalpha`
`=N=mg[sinalpha-0.8cosalpha]`
`N=mg sec alpha [tan alpha-0.8]`
`N=mgsec alpha [tan alpha-0.8]`
For `alpha gt tan^(-1) (0.8)`
`f_(A)gt f_(B)` for `alpha ge tan^(-1)(0.8)f_(A)=f_(B)`