A body of mass 10 kg is placed on rough surface, pulled by force F making an angle of `30^(@)` above the horizontal. If the angle of friction is also `30^(@)`, then the minimum magnitude of force F required to move the body is equal to ( take, `g=10 ms^(-2)`)

Options

A. 100 N
B. `50 sqrt(2)N`
C. `100sqrt(2)N`
D. 50N

Answer

D

Explanation

(d) `mu= tan 30^(@)=(1)/(sqrt(3))(30^(@)`=angle of friction)

`N=mg-F-sin 30^(@)=(100-(F)/(2))`
` implies" " (sqrt(3)F)/(2)=(1)/(sqrt(3))(100-(F)/(2))`
` implies (3F)/(2) =100-(F)/(2) implies F=50N`