JEE Mains · Physics · STD 11 - Gravitation
- JEE Mains 2024
- Hard
- MCQ
The gravitational potential at a point above the surface of earth is \(-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}\) and the acceleration due to gravity at that point is \(6.4 \mathrm{~m} / \mathrm{s}^2\). Assume that the mean radius of earth to be \(6400 \mathrm{~km}\). The height of this point above the earth's surface is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(1600 \mathrm{~km}\)
Step-by-step Solution
Detailed explanation
\( -\frac{G M_E}{R_E+h}=-5.12 \times 10^{-7} \ldots . \text { (i) } \)
\( \frac{G M_E}{\left(R_E+h\right)^2}=6.4 \ldots \text { (ii) }\)
By \((i)\) and \((ii)\)
\(\Rightarrow h=16 \times 10^5 \mathrm{~m}=1600 \mathrm{~km}\)
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