MHT CET · Physics · Rotational Motion

The moment of inertia of a thin uniform rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is

A $\frac{M L^{2}}{12}$
B $\frac{M L^{2}}{9}$
C $\frac{7 M L^{2}}{48}$
D $\frac{M L^{2}}{48}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{M L^{2}}{9}$

Step-by-step Solution

Detailed explanation

I_{C M} = \frac{M L^{2}}{12}

(about middle point)

Using parallel axis theorem.

∴

I = I_{C M} + M x^{2}

= \frac{M L^{2}}{12} + M {(\frac{L}{6})}^{2}

I = \frac{M L^{2}}{9}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The moment of inertia of a thin uniform rod of length L and mass M about an axis passing through a point at a distance of L3 from one of its ends and perpendicular to the rod is

Step-by-step Solution

The moment of inertia of a thin uniform rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is