TS EAMCET · Physics · Rotational Motion

A solid sphere and a disc of same mass ' \(M\) 'and radius ' \(R\) ' are kept such that their curved surfaces are in contact and their centers lie along the same horizontal line. The moment of inertia of the two body system about an axis passing through their point of contact and perpendicular to the plane of the disc is

A \(\frac{53 M R^2}{20}\)
B \(\frac{39 M R^2}{10}\)
C \(\frac{29 M R^2}{10}\)
D \(\frac{9 M R^2}{10}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{29 M R^2}{10}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text {} \mathrm{I}_1=\frac{2}{5} \mathrm{MR}^2+\mathrm{MR}^2 \\ = & \frac{7}{5} \mathrm{MR}^2\end{aligned}\) \(\mathrm{I}_2=\frac{1}{2} \mathrm{MR}^2+\mathrm{MR}^2=\frac{3}{2} \mathrm{MR}^2\) \(\therefore\) Moment of inertia about point of contact,…

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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