Question

The Centres Of Two Identical Spheres Are $1m$ Apart If The Gravitational Force Between The spheres be $1N$, then what is the mass of each sphere? ($G=6.67\times {10}^{-11}N{m}^2/k{g}^2$)

Answer 1

Step 1: Given

Distance between the spheres, $r=1m$

Gravitational force between them, $F=1N$

Gravitational constant, $G=6.67\times {10}^{-11}N{m}^2/k{g}^2$

Step 2: Formula used

The gravitational force between two objects is given by, $F=G\frac{m_1{m}_2}{r^2}$, where $m_1$ and $m_2$ are the masses of the objects.

Step 2: Determine the mass of each sphere

The gravitational force between two objects is given by, $F=G\frac{m_1{m}_2}{r^2}$

But as the masses are equal, we can write:

$$\begin{gathered} F=G\frac{m^2}{r^2} \\ {m}^2=\frac{1N\times {\left(1m\right)}^2}{6.67\times {10}^{-11}} \\ m=1.255\times {10}^{5}Kg \end{gathered}$$

Therefore, the mass of each sphere is $1.255\times {10}^{5}Kg$.