COMEDK · Physics · 9. Gravitation

If the radius of earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would

A Increase by \(4 \%\)
B Increase by \(2 \%\)
C Decrease by \(4 \%\)
D Increase by \(1 \%\)

Verified Solution

Answer & Solution

Correct Answer

(A) Increase by \(4 \%\)

Step-by-step Solution

Detailed explanation

The acceleration due to gravity \(g\) on the surface of the earth is given by the formula \(g = \dfrac{GM}{R^2}\), where \(G\) is the gravitational constant, \(M\) is the mass of the earth, and \(R\) is the radius of the earth. Given that the mass \(M\) remains constant, \(g\)…

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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