COMEDK · Physics · 9. Gravitation

Assuming, \(g_{\text {(Moon) }}=\left(\frac{1}{6}\right) g_{\text {Earth }}\) and \(D_{\text {(Moon) }}=\left(\frac{1}{4}\right) D_{\text {Earth }}\), where \(g\) and \(D\) are the acceleration due to gravity and diameter respectively, the escape velocity from the Moon is

A \(\frac{11.2}{24} \mathrm{kms}^{-1}\)
B \(11.2 \times \sqrt{24} \mathrm{kms}^{-1}\)
C \(\frac{11.2}{\sqrt{24}} \mathrm{kms}^{-1}\)
D \(11.2 \times 24 \mathrm{kms}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{11.2}{\sqrt{24}} \mathrm{kms}^{-1}\)

Step-by-step Solution

Detailed explanation

As we know, escape velocity, \(v_{e}=\sqrt{2 g R}\) Let \(v_{m}\) be escape velocity from moon and \(v_{e}\) be the escape velocity from Earth. Then, \(\frac{v_{m}}{v_{e}}=\sqrt{\frac{2 \times g_{m} \times R_{m}}{2 \times g_{e} \times R_{e}}}\)…

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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