The gravitational potential at a point at height h from the surface of earth is `-6.50 xx 10^(7) J kg^(-1)`, and acceleration due to gravity is `7.2 m//s^(2)`. Calculate the value of h if radius of earth is 6400 km.

Options

A. 2,627 km
B. 3,627 km
C. 4,627 km
D. 1,900 km

Answer

A

Explanation

(R + h) = distance from centre of earth
`V = (-GM)/((R + h)) = -6.50 xx 10^(7) J kg^(-1)` …(i)
`a = + (GM)/((R+h)^(2)) = 7.2 m//s^(2)` …(ii)
Dividing (i) by (ii)
`(GM(R+h)^(2))/((R+h).GM) = (R+h) = (6.50 xx 10^(7))/(7.2) = 0.9027 xx 10^(7) m`
(R +h) = 9,027 km
Height of the point above earth surface
`h = 9,027 km - 6,400 km`
= 2,627 km