A planet is rotating around the sun with the orbital radius three times than that of earth. The time period of this planet will be (For earth, time period is 365 days )

Options

A. 1,862 days
B. 1,000 days
C. 1,500 days
D. 2,000 days

Answer

A

Explanation

As `T^(2) prop R^(3)`
`(T_(2)^(2))/(T_(1)^(2)) = (R_(2)^(3))/(R_(1)^(3))`
`(T_(2)^(2))/(T_(1)^(2)) = ((3)/(1))^(3) = 27`
`T_(2)^(2) = T_(1)^(2) xx 27`
`T_(2) = T_(1) xx sqrt(27)`
`= 365 xx sqrt(27) = 365 xx 5.1 = 1,862` days