JEE Mains · Physics · STD 11 - 7. gravitation

In the reported figure of earth, the value of acceleration due to gravity is same at point \(A\) and \(C\) but it is smaller than that of its value at point \(B\) (surface of the earth). The value of OA \(: AB\) will be \(x : y .\) The value of \(x\) is \(\ldots \ldots \ldots\)

A \(3\)
B \(5\)
C \(4\)
D \(6\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(4\)

Step-by-step Solution

Detailed explanation

\(g_{A}=\frac{G M(r)}{R^{3}}\) \(g_{c}=\frac{G M}{\left(R+\frac{R}{2}\right)^{2}}\) \(g_{A}=g_{C}\) \(\frac{ r }{ R ^{3}}=\frac{1}{\frac{9}{4} R ^{2}} \Rightarrow r =\frac{4 R }{9}\) so \(OA =\frac{4 R }{9} ; AB = R - r =\frac{5 R }{9}\) \(OA : AB =4: 5\)

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.

Same subject

Match List-I with List-II.

	List-I		List-II
A.	Coefficient of viscosity	I.	\(\left[ ML ^{-1} T^{-2}\right]\)
B.	Surface tension	II.	\(\left[ ML ^2 T^{-2}\right]\)
C.	Pressure	III.	\(\left[ ML ^0 T^{-2}\right]\)
D.	Surface energy	IV.	\(\left[ ML ^{-1} T^{-1}\right]\)

Choose the correct answer from the options given below :

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