A non uniform cylinderical rod of mass 5 kg , length 2 m and radius 0.1 m is having its center of mass at a distance 2 1 m from the centre and lying on the axis of the rod. The rod is kept in a liqu

Question

A non uniform cylinderical rod of mass 5 kg , length 2 m and radius 0.1 m is having its center of mass at a distance $\frac{1}{2} m$ from the centre and lying on the axis of the rod. The rod is kept in a liquid of uniform density $1400 kg / m^{3}$ . The moment of inertia of the rod about the centre of mass is $4 kg - m^{2}$ . Find the angular acceleration (in SI unit) of point A of the rod just after the rod is released from the position shown in figure.

TestHub · Accepted Answer

Volume of rod ( V ) = π r 2 L = π × ( 0.1 ) 2 × 2 = 0.02 π m 3 F B ​ = ρ l i q u i d ​ V g = 1400 × 0.02 π × g = 28 π g N τ CM ​ = F B ​ × d = ( 28 π g ) × 0.5 = 14 π g N ⋅ m τ = I α α = I CM ​ τ CM ​ ​ α = 4 14 π g ​ = 3.5 π g r a d / s 2 α = 3.5 × 3.14 × 10 ≈ 110 r a d / s 2

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