A block with a square base measuring axa and height `h`, is placed on an inclined place. The coefficient of friction is `m`. The angle of inclination `(theta)` of the plane is gradually increased. The block will.

Options

A. topple before sliding if `mu gt (a)/(h)`
B. topple before sliding if `mu lt (a)/(h)`
C. slide before toppling if `mu gt (a)/(h)`
D. slide before toppling if `mu lt (a)/(h)`

Answer

A, D

Explanation

For topping before sliding
From translational equilibrium
`f_(l) gt mg sin theta`
`mu mg cos theta mg sin theta`
`mu gt tan theta`…(1)
taking rotation torque about `N` to topple
`mg sin theta xx (h)/(2) gt mg cos theta xx (a)/(2) rArr tan theta gt (a)/(h)` ....(2)
From (1) and (2) `mu gt (a)/(h)`
For slide before toppling
for translatinal motion
`mg sin theta gt mu mg cos theta tan theta gt mu` ...(1)
`mg cos theta xx (a)/(2) gt mg sin theta xx (h)/(2) rArr (2)/(h) gt tan theta` ...(2)
From (1) and (2) `(a)/(h) gt mu` or `mu lt (a)/(h)`.