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

\frac{1}{\sqrt{10}}

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100

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\frac{10}{\sqrt{10}}

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\sqrt{10}

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Solution

The correct option is D $\sqrt{10}$
By Kepler's law $T^{2} \propto r^{3}$
or, $\frac{T_{1}}{T_{2}} = {(\frac{r_{1}}{r_{2}})}^{3 / 2}$
$\frac{T_{1}}{T_{2}} = {(\frac{10^{13}}{10^{12}})}^{3 / 2}$
$\frac{T_{1}}{T_{2}} = 10 \sqrt{10}$

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The distance of two planets from the Sun are 1013 and 1012 m, respectively. The ratio of time periods of these two planets is

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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

The correct option is D $\sqrt{10}$
By Kepler's law $T^{2} \propto r^{3}$
or, $\frac{T_{1}}{T_{2}} = {(\frac{r_{1}}{r_{2}})}^{3 / 2}$
$\frac{T_{1}}{T_{2}} = {(\frac{10^{13}}{10^{12}})}^{3 / 2}$
$\frac{T_{1}}{T_{2}} = 10 \sqrt{10}$