A cylinder of height `H` and diameter `H//4` is kept on a frictional turntable as shown in Fig. The axis of the cylinder is perpendicular to the surface of the table and the distance of axis of the cylinder is `2H` from the centre of the table. The angular speed of the turntable at which the cylinder will start toppling (assume that friction is sufficient to prevent slipping) is

Options

A. `sqrt(g/2(1/2-H)`
B. `sqrt(g(1/2-H))`
C. `sqrt(g/(4H))`
D. `sqrt(g/(8H))`

Answer

D

Explanation

`N=mg` ……i
Net moment of all force about point `P` is zero. ` FH/2=mgh.8, omega=sqrt(g/(8H))`