Question

The distances of two planets from the sun are ${10}^{12}$ m and ${10}^{10}m$ respectively. The ratio of the time periods of these planets is

• A. 1000 : 1
• B. 100 : 1
• C. 10 : 1
• D. 1 : 1

Answer 1

The correct option is A 1000 : 1

Distance of two planets from sun, $r_1={10}^{12}m$ and $r_2={10}^{10}m$

Relation between time period $\left(T\right)$ and distance of the planet from the sun is,

$T^2\propto r^3$ and $T=r^{\frac{3}{2}}$

Therefore,

$\frac{T_1}{T_2}=(\frac{r_1}{r_2}{)}^{\frac{3}{2}}=(\frac{{10}^{12}}{{10}^{10}}{)}^{\frac{3}{2}}=\frac{1000}{1}$

So the ratio of the time periods of the planet is $1000:1$