Given that there is a relationship between the orbital radius of a planet and its period of revolution and that the periods of revolution of Mercury, Earth, Jupiter and Neptune are nearly 0.24,1,11.8 and 165 years. It follows that the period of revolution of

(A) Venus is less than 0.24 years old.

(B) Mars is less than 12 years old.

(C) Uranus is more than 165 years old.

(D) Uranus is less than 165 years old but more than 12 years old.

Of these the correct statement(s) is/are:

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A and C

Donly

C only

B and D

answer is B.

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Detailed Solution

Concept- The orbital radius of a planet increases with its distance from the sun. The longer it takes a planet to make one rotation around the sun, the larger its orbital radius.
The planets are first listed in order of increasing distance from the sun: 1) Mercury
2) Venus
3) Earth
4) Mars
5) Jupiter
6) Saturn
7) Uranus
8) Neptune
Mercury, Earth, Jupiter, and Neptune all have revolutions that last roughly 0.24, 1, 11.8, and 165 years, respectively. These facts suggest that the orbital radius and rotation period are precisely related to one another.
(A) Venus' period of revolution must be less than 024 years because it follows Mercury in the solar system. Consequently, this claim is untrue.
(B) Mars is less than 12 years - Because Mars orbits the Sun before Jupiter and after Earth, its period of revolution should be longer than Earth's (1 year) and shorter than Jupiter's (12 years) (11.8, approximately 12). Consequently, this claim is accurate.
(C) Uranus is older than 165 years - 165 years are listed as Neptune's period of revolution. Neptune comes after Uranus. Its revolution period hence cannot be longer than Neptune's. Consequently, this claim is untrue.
(D) Uranus has a period of revolution that is shorter than Neptune's since it comes before it, at less than 165 years but more than 12 years (12 years). Additionally, because Uranus comes after Jupiter, its revolutionary period is longer than Jupiter's (11.8, approximately 12). Consequently, this claim is accurate.
Hence, option 2 and 4 are correct.

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