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

Options

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

Answer

a

Explanation

The forces acting on the block are shown. Since the block is not moving forward for the maximum force F applied
`f cos 60^(@)=f=muN`
and `F sin 60^(f@) + mg =N`
form (i) and (ii) `f cos 60^(@)=mu[F sin 60^(@)+mg]`
`rarr f=(mu mg)/(cos 60^(@)-mu sin 60^(@))=(1)/(2sqrt(3)xxsqrt(3)xx10)(1/2)-(1)/(2sqrt(3))xx(sqrt(3)/(2))=5/1/4=20 N`