The Gravitational Potential... | JEE Main 2024

JEE-Main_2024

30.01.24_(S1)

Question

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 :

Select the correct option:

1600km

540km

1200km

1000km

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$$ \begin{aligned} & -\frac{G M_E}{R_E+h}=-5.12 \times 10^{-7} \\ & \frac{G M_E}{\left(R_E+h\right)^2}=6.4 \end{aligned} $$ By (i) and (ii) $$ \Rightarrow h=16 \times 10^5 \mathrm{~m}=1600 \mathrm{~km} $$

Question Tags

JEE Main

Physics

Medium

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