Question

The centers of two similar spheres are 1m apart. If the gravitational force between the two spheres is 1 newton, what is the mass of each sphere?

Answer 1

Step 1: Given data and diagram of the situation:

Given data:

Distance between two-sphere (r) = 1 m.

The gravitational force between two spheres = 1 newton.

The diagrammatic representation of the situation:

Step 2: Formula used

We know that the gravitational force of attraction between two masses is given by:

$F=\frac{G{m}_1{m}_2}{r^2}...........\left(a\right)$.

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

Step 3: Calculating the mass of the sphere

As, both the objects are similar,

Let the mass of each sphere be “M”

Putting all the given values in equation (a)

$$\begin{gathered} 1N=\frac{6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}\times M^2}{1m} \\ {M}^2=\frac{1k{g}^2}{6.67\times {10}^{-11}} \\ M=1.23\times {10}^{5}kg. \end{gathered}$$

Hence, the mass of each sphere is $1.23\times {10}^{5}kg.$