A block of mass `m` is placed at rest on a horizontal rought surface with angle of friction `phi`. The block is pulley with a force `F` at an angle `theta` with the horizontal. The minimum value of `F` required to move the block is

Options

A. `(m g sin phi)/(cos (theta - phi))`
B. `(m g cos phi)/(cos (theta - phi))`
C. `mg tan phi`
D. `mg sin phi`

Answer

A

Explanation

`mu = tan phi`
`N = m g - F sin theta`

`F cos theta = mu N = (tan phi) (m g - F sin theta)`
`= ((sin phi)/(cos phi)) (m g - F sin theta)`
On solving this equation,we get
`F = (mg sin phi)/(cos (theta - phi))`