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

Answer

A, C

Explanation

The block will remain stationary if
`mg sin theta = F cos theta `
`0.1 xx 10 sin theta = 1 cos theta `
`tan theta = 1`
`theta = 45^(@)`
`therefore` Option (a) is correct .

If `theta gt 45^(@)` , then force down the plane will become larger and the block will have tendency to slide down the plane . In order to prevent downward sliding of the block , the force of friction must act up the inclined plane , i.e., towards Q .
`therefore` Option (c) is correct .