If the distance of the Earth from the Sun is km, then the distance of an imaginary planet from the Sun, if its period of revolution is 2.83 years is: [2023]

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Solution

Q.
If the distance of the Earth from the Sun is $1.5 \times 10^{6}$ km, then the distance of an imaginary planet from the Sun, if its period of revolution is 2.83 years is: [2023]

1 $6 \times 10^{6} km$

2 $3 \times 10^{6} km$

3 $6 \times 10^{7} km$

4 $3 \times 10^{7} km$

Ans.
(2)

$T^{2} \propto R^{3} \Rightarrow {(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{R_{1}}{R_{2}})}^{3}$

$\Rightarrow {(\frac{1}{2.83})}^{2} = {(\frac{1.5 \times 10^{6}}{R_{2}})}^{3}$

$\Rightarrow R_{2} = {[{(2.83)}^{2} \times {(1.5 \times 10^{6})}^{3}]}^{1 / 3}$

$= 8^{1 / 3} \times 1.5 \times 10^{6} = 3 \times 10^{6} km$

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