At what height from the surface of Earth the gravitational potential and the value of g are `-5.4xx10^(7)J" "kg^(-1)and6.0ms^(-2)` respectively? Take the radius of the Earth as 6400 km.

Options

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

Answer

A

Explanation

Here `v=-5.4xx10^(7),g'=6.0ms^(-2)`,
`R=6.4xx10^(6)m`
As `v=-(GM)/((R+h))andg'=(GM)/((R+h)^(2))`
`therefore-5.4xx10^(7)=-(GM)/((R+h))and6.0=(GM)/((R+h)^(2))`
(or) `5.4xx10^(7)=(GM)/(R+h)and6.0=(GM)/((R+h)^(2))`
`therefore(5.4xx10^(7))/(6.0)=R+hor9xx10^(6)=R+h`
(or) `h=9xx10^(6)-R`
`=9xx10^(6)-6.4xx10^(6)`
`=2.6xx10^(6)m=2600km`