JEE Mains · Physics · STD 11 - 7. gravitation

The radius in kilometer to which the present radius of earth \(( R =6400\, km )\) to be compressed so that the escape velocity is increased \(10\) time is ............\(km\)

A \(64\)
B \(36\)
C \(72\)
D \(81\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(64\)

Step-by-step Solution

Detailed explanation

\(V _{ e }=\sqrt{\frac{2 Gm }{ R }}\) \(10 V _{ e }=\sqrt{\frac{2 Gm }{ R ^{\prime}}}\) \(\therefore 10=\sqrt{\frac{ R }{ R ^{\prime}}}\) \(\Rightarrow R ^{\prime}=\frac{ R }{100}=\frac{6400}{100}=64 km\)

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 the LIST-I with LIST-II.

LIST-I	LIST-II
(A) \(_0^1n + _{92}^{235}U \rightarrow _{54}^{140}Xe + _{38}^{94}Sr + 2_0^1n\)	(I) Chemical reaction
(B) \(2H_2 + O_2 \rightarrow 2H_2O\)	(II) Fusion with +ve Q value
(C) \(_1^2H + _1^2H \rightarrow _2^3He + _0^1n\)	(III) Fission
(D) \(_1^1H + _1^3H \rightarrow _1^2H + _1^2H\)	(IV) Fusion with -ve Q value

Choose the correct answer from the options given below :

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