A wedge with a rough groove in the shape of a quarter of a circle is kept on a smooth table (see figure). A small block is placed in the groove with a small clearance. The wedge is moved with an acceleration`sqrt(3)g` . If the block is to remain stationary relative to groove in the position shown, the coefficient of friction required can be:

Options

A. `(1)/(3)`
B. `(1)/(4)`
C. `(1)/(5)`
D. `(9)/(10)`

Answer

D

Explanation

`N cos 30^(@) = mg + f cos 60^(@)`
`N sin 30^(@) + f sin 60^(@) = mg sqrt(3)`
Put `f = mu N` and solve to get `mu = (1)/(sqrt(3))`
This means `mi ge (1)/(sqrt(3))`.