The solid semi-cylinder of mass m and radius R is rolled slowly through an angle $\theta$ by the horizontal force P. If the coefficient of static friction is ${\mu }_s,$ the angle $\theta$ at which the cylinder begins to slip on the horizontal surface as P gradually increased is $\theta ={\sin }^{-1}\left(\frac{3\pi {\mu }_s}{n-3\pi {\mu }_s}\right).$ Find ‘n’.