Class 10 Science I Gravitation

The mass of the earth is 6 x 10²⁴ kg. The distance between the earth and the Sun is 1.5x 10¹¹ m. If the gravitational force between the two is 3.5 x 10²² N, what is the mass of the Sun?

the given can be listed as

mass of earth , m = 6 x 10²⁴ kg.

distance between sun and earth is r = 1.5x 10¹¹ m

gravitational force F = 3.5 x 10²² N

$G=6.7\textrm{x}10^{-11}Nm^{2}kg^{-2}$

To find, mass of sun , M = ?

Solution -

Using Newtons law of gravitation we have ,

$F=\frac{GMm}{r^{2}}$

$M=\frac{Fr^{2}}{Gm}$

$M=\frac{3.5\textrm{x}10^{22}\textrm{x}(1.5\textrm{x}10^{11})^{2}}{6.7\textrm{x}10^{-11}\textrm{x}6\textrm{x}10^{24}}$

$M=\frac{3.5\textrm{x}10^{22}\textrm{x}1.5^{2}\textrm{x}10^{22}}{6.7\textrm{x}6\textrm{x}10^{13}}$

$M=\frac{3.5\textrm{x}2.25\textrm{x}10^{44}}{40.2\textrm{x}10^{13}}$

$M=\frac{7.875\textrm{x}10^{31}}{40.2}$

$M=0.1958\textrm{x}10^{31}=1.958\textrm{x}10^{30}=1.96\textrm{x}10^{30}kg$