The distance of two planets (Neptune and Saturn) from the sun are $10^{13} m$ and $10^{12} m$ respectively. Find the ratio of the time periods of the planets.

100 : 1

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1 : \sqrt{10}

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\sqrt{10} : 1

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10 \sqrt{10} : 1

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Solution

The correct option is D $10 \sqrt{10} : 1$
$R_{n} = 10^{13} m R_{s} = 10^{12} m T_{n}^{2} = R_{n}^{3} = {(10^{13})}^{3} = 10^{39} ∴ T_{n} = \sqrt{10^{39}}$
Similarly, $T_{s}^{2} = R_{s}^{3} = {(10^{12})}^{3} = 10^{36} T_{s} = \sqrt{10^{36}}$
${∴ T}_{n} : T_{s} = 10 \sqrt{10} : 1$

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The distance of two planets (Neptune and Saturn) from the sun are 1013m and 1012m respectively. Find the ratio of the time periods of the planets.

The correct option is D 10√10:1Rn=1013mRs=1012mT2n=R3n=(1013)3=1039∴Tn=√1039Similarly, T2s=R3s=(1012)3=1036Ts=√1036∴Tn:Ts=10√10:1

The distance of two planets (Neptune and Saturn) from the sun are $10^{13} m$ and $10^{12} m$ respectively. Find the ratio of the time periods of the planets.

The correct option is D $10 \sqrt{10} : 1$
$R_{n} = 10^{13} m R_{s} = 10^{12} m T_{n}^{2} = R_{n}^{3} = {(10^{13})}^{3} = 10^{39} ∴ T_{n} = \sqrt{10^{39}}$
Similarly, $T_{s}^{2} = R_{s}^{3} = {(10^{12})}^{3} = 10^{36} T_{s} = \sqrt{10^{36}}$
${∴ T}_{n} : T_{s} = 10 \sqrt{10} : 1$