If the time period of revolution of a planet is increased to `3sqrt(3)` times its present value, the percentage increase in its radius of the orbit of revolution is

Options

A. 50
B. 100
C. 200
D. 400

Answer

C

Explanation

According to Kepler's third law of planetary motion, `T^(2) prop R^(3) rArr ((R_(2))/(R_(1)))^(3)=((T_(2))/(T_(1)))^(2)`
Given, `T_(2) = 3 sqrt(3) T_(1) rArr T_(2)^(2) = 27 T_(1)^(2)`
`rArr ((R_(2))/(R_(1)))^(3) = 27 or (R_(2))/(R_(1)) = 3 rArr R_(2) = 3R_(1)`
The percentage increase in the radius of the orbit of revolution `= ((R_(2) - R_(1))/(R_(1)))100 = 200`