(a) Is the acceleration due to gravity of earth ‘g’ a constant? Discuss.
(b) Calculate the acceleration due to gravity on the surface of a satellite having a mass of $7.4\times 1022\ kg$ and a radius of $1.74\times 106\ m$ $(G=6.7\times10^{-11}\ Nm^2/kg^2)$. Which satellite do you think it could be?

(a). The value of gravitational acceleration $(g)$ is not constant at all the places on the surface of the earth. As we know the radius of the earth is minimum at its poles and maximum at its equator, the value of $g$ is maximum at the poles and minimum at the equator of the earth. As we go up from the surface of the earth, the distance from the center of the earth increases, and hence the value of gravitational acceleration$(g)$ decreases. The value of gravitational acceleration$(g)$ also decreases as we go down inside the earth.

(b). Mass of the planet $M=7.4\times10^{22}\ kg$

The radius of the planet $R=1.74\times10^6\ m$

$G=6.7\times10^{-11}\ Nm^2/kg^2$

Therefore, gravitational acceleration $g=\frac{GM}{R^2}$

$=\frac{6.7\times10^{-11}\ Nm^2/kg^2\times7.4\times10^{22}\ kg}{(1.74\times10^6\ m)^2}$

$=2.85\ m/s^2$

Therefore, gravitational acceleration due to gravity on the surface of a satellite is $2.85\ m/s^2$.

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Updated on: 10-Oct-2022

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