A light rigid rod $A B$ of length $3 l$ has a point mass $m$ at end $A$ and a point mass $2 m$ at end $B$ . It is kept on a smooth horizontal surface. Point $C$ is the center of mass of the system. Initially the system is at rest. The mass $2 m$ is suddenly given a velocity $v_{0}$ towards right. Take $Z$ axis to be perpendicular to the plane of the paper. [Points $C$ is center of mass].

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The magnitude of tension in the rod in subsequent motion is $\frac{2 m {v_{0}}^{2}}{9 l}$

The ratio of moment of inertia about $Z$ -axis at points $A$ and $B$ , $\frac{I_{z z}^{A}}{I_{z z}^{B}} = 2$

Point $C$ remains stationary during subsequent motion.

The minimum moment of inertia (about $Z$ -axis), $I_{z z}$ of the system is $5 m l^{2}$ .

answer is B, C.

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Detailed Solution

$2 m v_{0} l = 6 m l^{2} ω$

$∴ ω = \frac{v_{0}}{3 l}$

$T = 2 m ω^{2} l = \frac{2 m v_{0}^{2}}{9 l}$

And,

$I_{A} = 2 m {(3 l)}^{2} I_{B} = m {(3 l)}^{2}$

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