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At what height from the surface of earth...

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`:

A

`2600 km`

B

`1600 km`

C

`1400 km`

D

`2000 km`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, `V = - 5.4 xx 10^(7), g' = 6.0 ms^(-2)`
`R = 6.4 xx 10^(6)m`
As `V = - (GM)/((R + h))` and `g' = (GM)/((R + h)^(2))`
`:. - 5.4 xx 10^(7) = (GM)/((R + h))` and `6.0 (GM)/((R + h)^(2))`
or `5.4 xx 10^(7) = (Gm)/(R + h)` and `6.0 (GM)/((R + h)^(2))`
`:. (5.4 xx 10^(7))/(6.0) = R + h` or `9 xx 10^(6) = R +h`
or `h = 9 xx 10^(6) -R = 9 xx 10^(6) - 6.4 xx 10^(6)`
`= 2.6 xx 10^(6) m = 2600 km`
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