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

Answer

D

Explanation

Gravitational potential at some height `h` from the surface of the earth is given by
`V =-(GM)/(R+h)` ….(i)
And acceleration due to gravity at some height `h` from the earth surface can be given as
`g'=(GM)/((R+h)^(2))`....(ii)
From Eq. (i) and (ii), we get
`(|V|)/(g')=(GM)/((R+h))xx((R+h)^(2))/(GM)rArr(|V|)/(g')=R+h`....(iii)
`because V=-54xx10^(7)"J kg"^(-2)and g'=6 "ms"^(-2)`
Radius of earth, `R = 6400` km
Substitute these values in Eq. (iii), we get
`(5.4xx10^(7))/(6)=R+hrArr9xx10^(6)=R+h`
`rArr h=(9-6.4)xx10^(6)=26xx10^(6) " m"rArr h= 2600` km.