What is the value of applied force ‘F’ which is exerted at an angle `theta` with the horizontal on a block of mass ‘m’ placed on a horizontal rough surface, if the coefficient of static friction between the block and the surface is , such that the block is on the verge of moving horizontally?

Options

A. `(mu_(s)mg)/[(cos theta -mu_(s) sin theta)]`
B. `(mu_(s)mg)/[(cos theta +mu_(s) sin theta)]`
C. `mu_(s)mg`
D. `(mu_(s)mg)/[(mu_(s) cos theta + sin theta)]`

Answer

a

Explanation

Since the block is on the verge of moving `therefore` Limiting friction will act on the block For equilibrium,
`F cos theta =f_(1)=mu_(s)N`
`N=mg+F sin theta`
`from (i) and (ii)
`rarr F cos theta =mu_(s)[mg+f sin theta]`