A non-uniform cylinder 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 `l`. 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. `(pirhogl^(2)r^(2))/I`
B. `(pirhogl^(2)r^(2))/(4I)`
C. `(pirhogl^(2)r^(2))/(2I)`
D. `(3pirhogl^(2)r^(2))/(4I)`

Answer

B

Explanation

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