At what height from the surface of earth the gravitation potential and the value of `g` are `- 5.4 xx 10^(7) J kg^(-2)` and `6.0 ms^(-2)` respectively ? Take the radius of earth as `6400 km`:

Options

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

Answer

C

Explanation

Gravitation potential at a height h from the surface of earth, `V_h = -5.4 xx 10^7 J kg^(-2)`
At the same point acceleration due to gravity,
`g_h=6m s^(-2)`
` R=6400 km = 6.4 xx 10^6m` We know, `V_h = - (GM)/((R + h))`
` g_h = (GM)/((R + h)^2) =- (V_h)/(R+ h) rArr R+ h =- (V_h)/(g_h)`
` therefore h = - (V_h)/(g_h)- R = - ((-5.4 xx 10^7))/(6) - 6.4 xx 10^6 = 2600 km`