Question

Mass of two spheres is in the ratio 8:1. Assuming that both of them have same density, find the ratio of their radii.

Answer 1

Let radius of first sphere is $r_1$ and that of second sphere is $r_2$

Then, volume of first sphere = $\frac{4}{3}$ (${\pi r_1}^3)$ and volume of second sphere = $\frac{4}{3}$ (${\pi r_2}^3)$

Let density of both the spheres be d and mass be $m_1$ and $m_2$ respectively.

Then, $m_1$ = $\frac{4}{3}$ (${\pi r_1}^3)$ $\times$ d and $m_2$ = $\frac{4}{3}$ (${\pi r_1}^3)$ $\times$ d

Now, $\frac{m_1}{m_2}$ = 8

$\Rightarrow$ $\frac{\left(\frac{4}{3}\right({\pi r_1}^3)\times d)}{\left(\frac{4}{3}\right({\pi r_2}^3)\times d)}$ = 8

$\Rightarrow$ $\frac{{r_1}^3}{{r_2}^3}$ = 8

$\Rightarrow$ $\frac{r_1}{r_2}$= 2