JEE Mains · Physics · STD 11 - 7. gravitation

Given below are two statements: Statement \(I:\) Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement \(II:\) Acceleration due to earth's gravity is same at a height ' \(h\) ' and depth ' \(d\) ' from earth's surface, if \(h = d\). In the light of above statements, choose the most appropriate answer form the options given below

A Statement \(I\) is incorrect but statement \(II\) is correct
B Both Statement \(I\) and Statement \(II\) are incorrect
C Statement \(I\) is correct but statement \(II\) is incorrect
D Both Statement \(I\) and \(II\) are correct

Verified Solution

Answer & Solution

Correct Answer

(C) Statement \(I\) is correct but statement \(II\) is incorrect

Step-by-step Solution

Detailed explanation

\(g ^{\prime}=\frac{ g }{\left(1+\frac{ h }{ R }\right)^2}\) \(g^{\prime} = g 1-\frac {d }{R}\) Statement \(I\) is correct and Statement \(II\) is incorrect

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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