A non-uniform rod of mass `m`, length `l` and radius `r` is having its centre of mass at a distance `l//4` from the centre and lying on the axis of the cylinder. The cylinder is kept in a liquid of uniform density `rho`. The moment of inertia of the rod about the centre of mass is `I`. The angular acceleration of point `A` relative to point `B` just after the rod is released from the position as shown in the figure is

Options

A. ` (pi rho g l^2 r ^ 2 )/( I ) `
B. ` ( pi rho g l ^2 r ^2 )/(4 I ) `
C. ` ( pi rho g l ^ 2 r ^ 2 )/(2 I ) `
D. ` (3 pi rho g l ^ 2 r ^ 2 )/( 4 I ) `

Answer

B

Explanation

Torque about CM
`F_(b)(1)/(4)=I_(CM)alpha` or `alpha(1)/(I)(pir^(2))(1)(rho)(g)(1)/(4)=(pir^(2)1^(2)grho)/(4I)`