A small block of mass of `0.1 kg` lies on a fixed inclined plane `PQ` which makes an angle `theta` with the horizontal. A horizontal force of `1N` acts on the block through its centre of mass as shown in the figure. The block remains stationary if ( take `g=10 m//s^(2))`

Options

A. `theta=45^(@)`
B. `theta gt 45^(@)` and frictional force acts on the block towards `P`.
C. `theta gt 45^(@)` and frictional force acts on the block towards `Q`.
D. ` theta lt 45^(@)` and frictional force acts on the block towards `Q`.

Answer

A, C

Explanation

At `theta = 45^(@), mg sin theta = 1 xx cos theta`
At `theta gt 45^(@), mg sin theta = 1 xx cos theta` (friction acts upward)
At `theta lt 45^(@), mg sin theta = 1 xx cos theta` (Friction acts downward)
`x a = g sin theta - mu g cos theta`