Question

The distance of two planets from the Sun are ${10}^{13}$ and ${10}^{12}$m, respectively. The ratio of time periods of these two planets is?

• A. $\frac{1}{\sqrt{10}}$
• B. $100$
• C. $10\sqrt{10}$
• D. $\sqrt{10}$

Answer 1

The correct option is C $10\sqrt{10}$

By Kepler's law,

$T^2\alpha R^3$

So,

$\frac{T_{reprove}^2}{T_{square}^2}=\frac{({10}^{13}{)}^3}{({10}^{12}{)}^3}$

$\Rightarrow \frac{T_{reprove}}{square}={\left(\frac{{10}^{13}}{{10}^{12}}\right)}^{\frac{3}{2}}$

$\Rightarrow \frac{T_{reprove}}{square}=\frac{10\sqrt{10}}{1}=\frac{31.6}{1}$