A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is : [Take g = 10 m/s²]

∑F=0

2+mgsin30 = μmgcos30^o  .............................(i)

10 = mgsin30 + μmgcos30^o   .....................(ii)

Adding eq (i) and (ii), we get

12 = 2μmgcos30

6 = μmgcos30  .......................................(iii)

4 = mgsin30   .............................................(iv)

From eq (iii) and (iv), we get

3​/2 = μ×cot30^o 

3/2​ = μ$\times$$\sqrt{3}$

μ =$\raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$