Question

At what height from the surface of earth the gravitation potential and the value of g are $- 5.4 \times 10^7 \, J \, kg^{-2}$ and $6.0 \, ms^{-2}$ respectively ? Take the radius of earth as $6400 \,km$ :

• A. 1600 km
• B. 1400 km
• C. 2000 km
• D. 2600 km

Answer 1

Answer: (D)

2600 km

Answer 2

$V = \frac{-GM}{R +h} = -5.4 \times 10^{7}$ ....(1)
and $g = \frac{GM}{(R + h)^2} = 6$ ......(2)
dividing (1) and (2)
$\Rightarrow \, \frac{5.4 \times 10^{7}}{(R + h)} = 6$
$\Rightarrow \, R + h = 9000 \; km$ so $h = 2600 \; km$