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>>Gravitational Potential Energy
>> $At what height from the surface of earth$

Question

At what height from the surface of earth the gravitation potential and the value of $g$ are $- 5.4 \times 10^{7} J k g^{- 2}$ and $6.0 m s^{- 2}$ respectively? Take the radius of earth as $6400 k m$ .

A

$2600 k m$

B

$1600 k m$

C

$1400 k m$

D

$2000 k m$

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Updated on : 2022-09-05

Solution

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Correct option is A)

$V = - \frac{G M}{R + h} = - 5.4 \times 1 0^{7}$ ....... (1)

$g = \frac{G M}{( R + h ) ^{2}} = 6$ ...... (2)

Dividing the two equations, we get:

$\Rightarrow \frac{5 . 4 \times 1 0 ^{7}}{( R + h )} = 6$

$\Rightarrow R + h = 9000 k m$

$\Rightarrow h = 2600 k m$

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