NEET 2024 — Physics solution

NEET2024Physics

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

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

Solution

For a thin rod rotated about its centre perpendicular to its length, $I = \frac{M L ^{2}}{12}$ .

Substituting $I = 2400$ g cm $^{2}$ and $M = 400$ g:

$L^{2} = \frac{12 \times 2400}{400} = 72$ cm $^{2}$

$∴ L = 72 \approx 8.49$ cm $\approx 8.5$ cm.

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