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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 $ρ$ . 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.

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$\frac{π ρ g l^{2} r^{2}}{4 I}$

$\frac{π ρ g l^{2} r^{2}}{2 I}$

$\frac{3 π ρ g l^{2} r^{2}}{4 I}$

$\frac{π ρ g l^{2} r^{2}}{I}$

answer is B.

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Detailed Solution

Torque about CM

$F_{b} \frac{1}{4} = l α \Rightarrow α = \frac{l}{I} (π r^{2}) (l) (p) (g) \frac{1}{4} \Rightarrow α = \frac{π r^{2} l^{2} g p}{4 I}$

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