At what height from the surface of earth the gravitation potential and the value of g are −5.4 × 10⁷ J kg⁻² and 6.0 ms⁻² respectively? Take the radius of earth as 6400 km:

2600 km

V_{at height h} = -\(\frac{GM_e}{R_e + h}\) ----------(1)

g_h = \(\frac{GM_e}{(R_e + h)^2}\) = 6 ----------(2)

\(\frac{V_{\text{at height h}}}{g_h}\) = R_e + h = \(\frac{5.4 × 10^7}{6}\)

R_e + h = 9 × 10⁶

h = 9 × 10⁶ - 6.4 × 10⁶ 

   = 2600km