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Calculate the acceleration due to gravit...

Calculate the acceleration due to gravity at a height of 1600 km from the surface of the Earth. (Given acceleration due to gravity on the surface of the Earth `g_(0) = 9.8 ms^(-2)` and radius of earth, R = 6400 km).

A

`6.27 m//s^2`

B

`3.28 m//s^2`

C

`5.36 m//s^2`

D

`4.86 m//s^2`

Text Solution

Verified by Experts

The correct Answer is:
A
Given
Height from the surface of the Earh, h = 1600 km.
Radius of the Earth, R = 6400 km.
Acceleration due to gravity on the surface of the Earth `g_(0) = 9.8 ms^(-2)`
`therefore` acceleration due to gravity at the given height,
`" "g = (g_(0))/((1 + (h)/(R))^(2))=(9.8)/((1 + (1600)/(6400)))=(9.8 xx 16)/(25)=6.272 ms^(-2)`
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