The gravitational potential at a point above the surface of earth is -5.12 × 10 7 J / kg and the acceleration due to gravity at that point is 6.4 m / s 2 . Assume that the mean radius of earth to be 6400 km . The height of this point above the earth's surface is :

Physics · Gravitation

JEE Main 2024 — 30 January, Shift 1 — Question 38

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 km . The height of this point above the earth's surface is :

Option A:
1600 km
Correct
Option B:
540 km
Option C:
1200 km
Option D:
1000 km

Answer: A

Step-by-step solution

$-\frac{G M_{E}}{R_{E}+h}=-5.12 \times 10^{-7}$ $\frac{G M_{E}}{\left(R_{E}+h\right)^{2}}=6.4 \ldots \text { (ii) }$

By (i) and (ii) $\Rightarrow h=16 \times 10^{5} \mathrm{~m}=1600 \mathrm{~km}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 30 January, Shift 1
Subject: Physics
Chapter: Gravitation
Topic: Gravitational Potential Energy and Potential