Question

A satellite whose distance from the centre of the planet is four times the radius of the planet is revolving around it. If the acceleration due to gravity on the surface of the planet is 5 metre per second square calculate the magnitude of the acceleration due to gravity of satellite​

Answer 1

Given :

Distance of satellite = 4R

• where R is the radius of planet and distance is measured from the centre of the planet

Acceleration due to gravity at the surface of the planet is 5 m/s²

To Find :

Acceleration due to gravity of satellite.

Solution :

Acceleration due to gravity of a planet whose mass is M and radius is R at a height of H from the surface is given by

$:\implies\:\underline{\boxed{\bf{\purple{g'=\dfrac{g}{\left(1+\dfrac{H}{R}\right)^2}}}}}$

• g denotes acceleration due to gravity of planet at surface

Distance of the satellite from the surface of the planet will be;

→ H = d - R

→ H = 4R - R

→ H = 3R

By substituting the given values;

$\sf:\implies\:g'=\dfrac{5}{\left(1+\dfrac{3R}{R}\right)^2}$

$:\implies\:g'=\dfrac{5}{\left(1+3\right)^2}$

$\sf:\implies\:g'=\dfrac{5}{(4)^2}$

$\sf:\implies\:g'=\dfrac{5}{16}$

$:\implies\:\underline{\boxed{\bf{\gray{g'=0.312\:ms^{-2}}}}}$