Question

The gravitational potential at a point above the surface of earth is $-5.12 \times 10^7 \, \text{J} / \text{kg}$ and the acceleration due to gravity at that point is $6.4 \, \text{m/s}^2$. Assume that the mean radius of earth to be $6400 \, \text{km}$. The height of this point above the earth’s surface is:

• A. 1200 km
• B. 540 km
• C. 1600 km
• D. 1000 km

Answer 1

Answer: (C)

1600 km

Answer 2

Using the formula for gravitational potential and gravitational field:

$\frac{-G M_E}{R_E + h} = -5.12 \times 10^7$ and $\frac{G M_E}{(R_E + h)^2} = 6.4$

$16 \times 10^5$

(This is in meters)

To convert, divide by 1000:

$h = 1600 \, \text{km}$