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. 1,600 km
B. 1,400 km
C. 2,000 km
D. 2,600 km

Answer

D

Explanation

gravitational potential
`V = (-GM)/((R+h))`
`g. = (GM)/((R+h)^(2)) rArr GM = g. (R+h)^(2)`
`|V| = g.(R+h)`
`h = +(|V|)/(g.) - R = (5.4 xx 10^(7))/(6) - 6,400 xx 10^(3)`
`= 2,600 xx 10^(3) = 2,600 km`