एक ग्रह का द्रव्यमान पृथ्वी के द्रव्यमान का \(\frac{1}{10}\) वाँ भाग है तथा इसका व्यास पृथ्वी के व्यास का आधा है। उस ग्रह पर गुरुत्वीय त्वरण है:

A \(9.8 \mathrm{~m} \mathrm{~s}^{-2}\)
B \(4.9 \mathrm{~m} \mathrm{~s}^{-2}\)
C \(3.92 \mathrm{~m} \mathrm{~s}^{-2}\)
D \(19.6 \mathrm{~m} \mathrm{~s}^{-2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(3.92 \mathrm{~m} \mathrm{~s}^{-2}\)

Step-by-step Solution

Detailed explanation

\(g^{\prime}=\frac{G M^{\prime}}{R^{\prime 2}}=\frac{G M}{10\left(\frac{R}{2}\right)^2}\) \(=\frac{4}{10} \frac{G M}{R^2}=0.4 \times 9.8\)

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

Explore more questions on app

From NEET

सूची \(I\) को सूची \(II\) के साथ सुमेलित करो-

List \(I\)	List \(II\)
\(A\) टायफॉइड	\(I\) कवक
\(B\) लीशमैनियता	\(II\) सुत्रकृमि
\(C\) रिंगवर्म	\(III\) प्रोटोजोआ
\(D\)फाइलेरिएसिस	\(IV\) जीवाणु

निम्न विकल्पों से सही उत्तर का चयन करोः

NEET 2024 Medium

Explore more questions on app