Question

Determine the gravitational force of interaction between two spheres of masses 20 kg and 50 kg and radii 3 m and 2 m, respectively. The separation between their centers is 10 m.

Answer 1

Step 1: Given data:
Mass of the first sphere $\left(\mathrm{m}1\right)=20\mathrm{kg}.$
Mass of the second sphere $\left(\mathrm{m}2\right)=50\mathrm{kg}.$
Distance of separation between the centers $\left(\mathrm{r}\right)=10\mathrm{m}$.

Step 2: Calculating gravitational force
Gravitational force of interaction between two masses is.

$\mathrm{F}=\frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{{\mathrm{r}}^2}$
Where,
$\mathrm{G}–\mathrm{Gravitational}\mathrm{constant}.$
Newton’s law of gravitation can also apply for spheres. Because, in sphere all mass will be concentrated in center of the sphere. So, it taken as point on mass and Radius of the spheres can’t be affect mass of the sphere.

$$\begin{gathered} \mathrm{F}=\frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{{\mathrm{r}}^2}=\frac{(6.6743\times {10}^{-11})\left(20\right)\left(50\right)}{{\left(10\right)}^2} \\ {\text{F =6.67×10}}^{-10}\text{N} \end{gathered}$$

Hence the gravitational force of interaction between two spheres of masses is $6.67\times \times {10}^{-10}N$