Q118 / 200 · NEET 2024 · Physics

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is $2400 \mathrm{~g} \mathrm{~cm}^2$. The length of the 400 g rod is nearly:

A
17.5 cm
B
20.7 cm
C
72.0 cm
Correct answer
D
8.5 cm

Solution

Moment of inertia of rod $=I=\frac{m \ell^2}{12}$ $\begin{aligned} & \Rightarrow \quad 2400=400 \frac{\ell^2}{12} \\ & \Rightarrow \quad 72=\ell^2 \\ & \Rightarrow \quad \ell=\sqrt{72}=8.48 \mathrm{~cm} \simeq 8.5 \mathrm{~cm}\end{aligned}$

Hence, the correct answer is option: 'D'.

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