A uniform cube of side 'b' and mass `M` rest on a rough horizontal table. A horizontal force `F` is applied normal to one of the face at a point, at a height `3b//4` above the base. What should be the coefficient of friction `(mu)` between cube and table so that is will tip about an edge before it starts slipping ?
.

Options

A. `mu gt (2)/(3)`
B. `mu gt (1)/(3)`
C. `mu gt (3)/(2)`
D. none

Answer

A

Explanation

For body diagram when block is about to tip
For block not to slip `F_(l) ge F`
`mu N ge F`
`mu mg ge F` …..(1)
to tip about edge
taking moment of force about edge `A`
`F xx (3b)/(4) - mg xx (b)/(2) = 0`
`F = (2mg)/(3)` .....(2)
from (a) & (2)
`mu mg ge (2)/(3) mg rArr mu ge (2)/(3)`.