At a point above the surface of the earth, the gravitational potential is `-5.12xx10^(7)JKg^(-1)` and the acceleration due to gravity is `6.4 ms^(-2)`. Assuming the mean radius of the earth to be 6400 km, calculate the heights of this point above the earth's surface.

Options

A. 1200 km
B. 1600 km
C. 1800 km
D. 2400 km

Answer

B

Explanation

Gravitational potential
`v=(GM)/(R+r)`
Also `g.=g.=(GM)/((R+h)^(2))`
Now
`V==-(GM)/((R+h)^(2))(R_h)=-g.(R+h)`
`:.-5.12xx10^(7)=-6.4(6400+h)`
`xx10^(3)`
Solving we get h=1600km