Question

if acceleration due to gravity on a planet is 6.6mper seconds square and its radius is 4 x 10 power 6m then mass of the planet is

Answer 1

HELLO THERE!

The equation relating acceleration due to gravity, mass and radius is:

$g = \frac{GM}{R^{2}}$

or,

$M = \frac{gR^{2}}{G}$

Where, g is the acceleration due to gravity in the planet, G is Universal Gravitational Constant, and R is the Radius of the Planet.

We know, G = 6.67 x 10⁻¹¹ Nm²kg⁻²

Given, g = 6.6 m s⁻²

R = 4 x 10⁶ m

Putting these values in the equation,

[tex] M = \frac{gR^{2}}{G} \\\\\implies M = \frac{6.6\times(4\times10^{6})^{2}}{6.67\times10^{-11}} kg \\\\\implies M = 1.58\times10^{24}kg [/tex]

So, we got the mass M of the planet.

HOPE THIS HELPS...

Thanks!