Question: The gravitational potential at height h above the earth's surface is – 5.12 × 10<sup>7</sup> J/kg an...

Question

The gravitational potential at height h above the earth's surface is – 5.12 × 10⁷ J/kg and acceleration due to gravity at this point is 6.4 m s². If radius of the earth is 6400 km, the value of h is :

Answer 1

Solution

Gravitational potential

v = – $\frac { \mathrm { GM } } { \mathrm { R } + \mathrm { h } }$ ; g ' = $\frac { \mathrm { GM } } { ( \mathrm { R } + \mathrm { h } ) ^ { 2 } }$

Now, v = – $\frac { \mathrm { GM } } { ( \mathrm { R } + \mathrm { h } ) ^ { 2 } }$ (R + h) = – g ' (R + h)

\ – 5.12 × 10⁷ = – 6.4 (6400 + h) × 10³

h = 1600 km.