Question

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.
(B) Mars is less than 12 years.
(C) Uranus is more than 165 years.
(D) Uranus is less than 165 years but more than 12 years.
Of these the correct statement(s) is/are:
1) A and C
2) D only
3) C only
4) B and D

Answer 1

Hint:The farther the planet is from the sun, the greater is its orbital radius. Greater the orbital radius, greater the time taken by the planet to complete one revolution around the sun.

Complete step by step answer:
First, we list the planets according to their increasing distance from the sun,
1) Mercury
2) Venus
3) Earth
4) Mars
5) Jupiter
6) Saturn
7) Uranus
8) Neptune
Periods of revolution of Mercury, Earth, Jupiter and Neptune are given as 0.24, 1, 11.8 and 165 years approximately. From this information, we can imply that the orbital radius and the period of revolution are directly proportional to each other.
(A) Venus is less than 0.24 years – Since, Venus comes after Mercury, its period of revolution cannot be less than 024 years. Hence, this statement is false.
(B) Mars is less than 12 years – Since Mars comes after Earth and before Jupiter, its period of revolution should be greater than that of Earth (1 year) and less than that of Jupiter (11.8, approximately 12). Hence, this statement is true.
(C) Uranus is more than 165 years – The period of revolution of Neptune is given as 165 years. Uranus comes before Neptune. Therefore, its period of revolution cannot be greater than Neptune. Hence, this statement is false.
(D) Uranus is less than 165 years but more than 12 years – Uranus comes before Neptune so its period of revolution is less than Neptune (12 years). Also Uranus comes after Jupiter so its period of revolution is greater than Jupiter (11.8, approximately 12). Hence, this statement is true.
Hence,statements B and D are true.


Note:Since the period of revolution increases as the orbital radius increases, we can say that the period of revolution of a planet is directly proportional to its orbital radius.