Answer to Question #254184 in Physics for sabby

Question

The centers of two masses are 5m apart. The masses exert a gravitational force of

2.4x10^-4 N on each other. Find the masses if one is three times the mass of the other.

Answer 1

Given:

$F=2.4*10^{-4}\:\rm N$

$m_1=3m_2$

$r=5\:\rm m$

The gravity force is given by:

$$F=G\frac{m_1m_2}{r^2}$$

We get

$$F=G\frac{3m_2^2}{r^2}$$

$$m_2=\sqrt{\frac{r^2F}{3G}}=\sqrt{\frac{5^2*2.4*10^{-4}}{3*6.67*10^{-11}}}=5476\:\rm kg$$

$$m_1=3m_2=3*5476\:\rm kg=16428\:\rm kg$$