What is the maximum value of the force F such that the block shown in the arrangement, does not move?

Options

A. 20N
B. 10N
C. 12N
D. 15N

Answer

A

Explanation

The forces acting on the block are shown. Since the block is not moving forward for the maximum force F applied, therefore
`F cos 60^@=f=muN` …(i) (Horizontal Direction)
and `F sin 60^@ + mg =N` …(ii)
From (i) and (ii)

`Fcos60^@=mu[F sin 60^@+mg]`
`impliesF=(mumg)/(cos 60^@-mu sin 60^@)`
`=((1)/(2sqrt3)xxsqrt3xx10)/(1/2-(1)/(2sqrt3)xxsqrt3/2)=(5)/(1/4)=20N`