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

Explanation

The body diagram of the block is shown in Clearly
`R = mg + F sin 60^(@)`
The block will not move , when `F cos 60^(@) le f` (force of friction)
`(F)/(2) le mu R `
`(F)/(2) le mu (mg + F sin 60^(@))`
`(F)/(2) le (1)/(2 sqrt(3))(sqrt3g + F sqrt3/2)`
`(F)/(2) le ((g)/(2) + (F)/(4))` or `(F)/(2) - (F)/(4) le(g)/(2)` or `F//4 le (g)/(2)`
`F le 2 g`
Hence `F_(max) = 2 g = 2 xx 10 = 20 N`