MHT CET · Physics · Rotational Motion

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is \(\mathrm{K}_{\mathrm{c}}\). Radius of gyration of the same disc about a diameter of the disc is \(K_d\). The ratio \(K_c: K_d\) is

A \(\sqrt{2}: 1\)
B \(1: \sqrt{2}\)
C \(2: 1\)
D \(1: 4\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{2}: 1\)

Step-by-step Solution

Detailed explanation

Let the radius of the disc be \(\mathrm{R}\)
\(\begin{array}{ll}\therefore \mathrm{K}_{\mathrm{c}}=\frac{\mathrm{R}}{\sqrt{2}} \\\therefore \mathrm{K}_{\mathrm{d}}=\frac{\mathrm{R}}{2}\end{array}\)
Taking the ratio,
\(\therefore \frac{\mathrm{K}_{\mathrm{c}}}{\mathrm{K}_{\mathrm{d}}}=\frac{{\frac{\mathrm{R}}{\sqrt{2}}}\frac{\mathrm{R}}{2}}=\frac{\sqrt{2}}{1}\)

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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