Question

What is the force of gravity on a body of mass 150 kg lying on the surface of the earth?
(Mass of earth =$6\times {10}^{24}$ kg; Radius of earth = $6.4\times {10}^{6}m;G=6.7\times {10}^{-11}N{m}^2/k{g}^2$)

Answer 1

The formula for the force (F) according to law of gravitation is given by,

F = $\frac{G\times M_E\times m_{obj}}{R^2}$

Given :

Mass of earth, $M_E$ =$6\times {10}^{24}kg$;

Radius of earth, R = $6.4\times {10}^{6}m$;

Gravitation, G =$6.7\times {10}^{-11}\frac{N{m}^2}{k{g}^2}$

Mass of a body $m_{obj}$ = 150 kg

Plug in the values to the formula,

F =$\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 150}{{(6.4\times {10}^6)}^2}$

F= $\frac{6.7\times 6\times 150\times {10}^{(-11+24)}}{({6.4}^2\times {10}^{6\times 2})}$

F = $\frac{6030\times {10}^{13}}{40.96\times {10}^{12}}$

F = $147.21\times {10}^{(13-12)}$ = $147.21\times 10$
F= 1472 N