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

Let F be the maximum value of force applied when the block of `m=sqrt3kg` does not move on the rough surface.
R=normal reaction. Normal to surface
or v `R=F sin 60^(@)+mg`
f=friciton of friction
`mu R=F cos 60^(@)`
`mu(F sin 60^(@)+mg)=F cos 60^(@)`
`mu F sin 60^(@)+mumg=Fcos60^(@)`
or `F=(mumg)/(cos 60^(@)-mu sin 60^(@))`
`=((1)/(2sqrt3)xxsqrt3xx10)/((1)/(2)-((1)/(2sqrt3)xx(sqrt3)/(2)))=(5)/((1)/(2)-(1)/(4))=5xx4=20N`
Maximum value of force =20N