Question

The gravitational force between two objects that are 2.1 times 10^-1 m apart is 3.2 times 10^-6 N. If the mass of one object is 55kg what is the mass of the other object?

Answer 1

Answer:

Mass of the other object is 38.45 kg.

Explanation:

Given:

The gravitational force between two objects is, $F=3.2\times 10^{-6}$ N

Mass of one object is, $m_{1}=55\ kg$

Distance between the objects is, $r=2.1\times 10^{-1}\ m$

Gravitational constant is, $G =6.674\times 10^{-11}\ m^3 kg^{-1}s^{-2}$

Let the mass of the other object be $m_{2}\ kg$

Gravitational force is given as:

$F=\frac{Gm_1m_2}{r^2}$

Plug in the given values and solve for $m_2$. This gives,

$3.2\times 10^{-6}=\frac{6.674\times 10^{-11}\times 55\times m_2}{(2.1\times 10^{-1})^2}\\3.2\times 10^{-6}=\frac{6.674\times 10^{-11}\times 55\times m_2}{0.0441}\\3.2\times 10^{-6}=8.3236\times 10^{-8}m_2\\m_2=\frac{3.2\times 10^{-6}}{8.3236\times 10^{-8}}= 38.45\ kg$

Therefore, the mass of the other object is 38.45 kg.