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  4. At what height from the surface of earth the gravitation potential and the value of g are - 5.4 × 107 J kg-2 and 6.0 ms-2 respectively ? Take the radius of earth as 6400 km :

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Q. At what height from the surface of earth the gravitation potential and the value of g are $- 5.4 \times 10^7 \, J \, kg^{-2}$ and $6.0 \, ms^{-2}$ respectively ? Take the radius of earth as $6400 \,km$ :

NEETNEET 2016Gravitation

Solution:

$V = \frac{-GM}{R +h} = -5.4 \times 10^{7}$ ....(1)
and $g = \frac{GM}{(R + h)^2} = 6 $ ......(2)
dividing (1) and (2)
$\Rightarrow \, \frac{5.4 \times 10^{7}}{(R + h)} = 6 $
$\Rightarrow \, R + h = 9000 \; km $ so $h = 2600 \; km $