Question

The period of revolution of planet A around the sun is 27 times that of planet B. The distance of planet A from the sun is how many times greater than that of B from the sun?

Options

• 8

• 6

• 4

• 3

Answer 1

8

Explanation:

We know, \[T^2\propto R^3\]

\[\therefore\quad\left(\frac{\mathrm{R}_1}{\mathrm{R}_2}\right)^3=\left(\frac{\mathrm{T}_1}{\mathrm{T}_2}\right)^2=\left(\frac{27\mathrm{T}_2}{\mathrm{T}_2}\right)^2=\left(\frac{27}{1}\right)^2\]

\[\therefore\quad\frac{\mathrm{R}_1}{\mathrm{R}_2}=\left(27\right)^{\frac{2}{3}}=9\]

\[\therefore\quad\mathrm{R}_{1}=9\mathrm{R}_{2}\]

\[\therefore\quad\mathrm{R_{1}-R_{2}=9R_{2}-R_{2}=8R_{2}}\]