Question

Prove that gravitational force of attraction between two boys (each weighing $35kg$ ) sitting $1$ metre apart is almost negligible as compared to the force of gravitation between either of the boys and the earth. Mass of the earth $=6\times {10}^{24}kg$ and radius of the earth $=6.37\times {10}^{6}m$
Take $G=6.67\times {10}^{-11}SI$ units.

Answer 1

The gravitational force is given as

$F=G\frac{M_1{M}_2}{r^2}$

Substituting the values of mass, gravitational constant and radius we get the two forces

$F=6.67\times {10}^{11}\frac{35\times 35}{1}$

$=8.17\times {10}^{14}N$

Force between earth and boy is

$F=6.67\times {10}^{11}\times \frac{6\times {10}^{24}\times 35}{6.37\times {10}^6}$

$=2.19\times {10}^{31}N$