Question

The gravitational force between two people is 1.50 10^-6N. If person A has a mass of 82.0kg and is 0.600m away from person B person Bs mass is ___kg?

Answer 1

According to the Newton's gravity law, the force between two bodies with masses $m_1$ and $m_2$ separated by the distance $r$ is the following:

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

where $G = 6.67\cdot 10^{-11} m^3kg^{-1}s^{-2}$ is the gravitational constant. Expressing $m_1$ from this formula get:

$$m_1 = \dfrac{r^2F}{m_2G}$$

Substituting numerical values:

$$m_1 = \dfrac{0.6^2\cdot 1.5\cdot 10^{-6}}{82\cdot 6.67\cdot 10^{-11}} \approx 98.7kg$$

Answer. m2 = 98.7 kg.