Question

Find the acceleration due to gravity at a height of 400 km above the surface of the earth.Given radius of earth=6400 km and acceleration due to gravity at the surface of the earth is 9.8/s2.

Answer 1

Hi mate.


Thanks for asking this question.


Here is your answer,





Given :


$h = 400km$

$r = 6400km$

$g = 9.8 \frac{m}{ {s}^{2} }$

$gh = ac. \: due \: to \: gravity \: t \: height \: \\ \: \: \: \: \: \: \: \: \: \: \: h = - -$


We know that,


$gh = g \times { (\frac{r}{r + h} )}^{2}$

$gh = 9.8 \times { (\frac{6400}{6400 + 400}) }^{2}$

$gh = 9.8 \times { (\frac{6400}{6800} )}^{2}$

$gh = 9.8 \times { (\frac{16}{17} )}^{2}$

$gh = 9.8 \times ({0.9411)}^{2}$

$gh = 9.8 \times 0.8856$

$gh = 8.6788 \frac{m}{ {s}^{2} }$








Thank you.






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Answer 2

Given :

Radius of earth , R = 6400 km .

Acceleration due to gravity at the surface of the earth , $g=9.8\ m/s^2$ .

To Find :

The acceleration due to gravity at a height of 400 km .

We know :

Acceleration at height h is given by :

$g_h=g(\dfrac{R}{R+h})^2$

Putting all given values :

$g_h=9.8\times (\dfrac{6400}{6400+400})^2\\\\g_h=9.8\times( \dfrac{6400}{6800})^2\\\\g_h=8.68\ m/s^2$

Hence , this is the required solution .

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