A body is sliding down an inclined plane `(mu = (1)/(2))`. If the normal reaction is twice that of the resultant downward force along the incline , the inclination of plane is

Options

A. `15^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

C

Explanation

`N = mg cos theta , f = mu mg cos theta`
Net downward force acting along the incline is
`mg sin theta - f = mg sin theta - mu mg cos theta`
Given
`N = 2(mg sin theta - mu mg sin theta)`
`mg cos theta = 2( mg sin theta - mu mg cos theta)`
` cos theta = 2 sin theta - 2 mu cos theta = 2 sin theta - 2 xx (1)/(2) cos theta`
` tan theta = 1 rArr theta = 45^(@)`