A block of mass m is pulled on an incline surface having coefficient of friction `mu=1 &` angle of inclination `theta=30^(@)`, with the horizontal, such that required external force is minimum. The angle made by this force with the incline is :

Options

A. `45^(@)`
B. `30^(@)`
C. `75^(@)`
D. `53^(@)`

Answer

A

Explanation

`F cosa-muN-mg sintheta=0` .....(i)
`& N+F sinalpha-mg cos theta=0` ....(ii)
Solving (i) `&` (ii)
`F=(mg sin theta+mu mg costheta)/(cos alpha + sinalpha)`
`F_("min")=(mg sin theta+ mumg cos theta)/(sqrt(1+mu^(2))`
`& tanalpha=mu rArr alpha=tan^(-1)mu`