If the time period of a satellite in the orbit of radius r around a planet is T. Then the time period of a satellite in orbit of radius 4r is T = .....

Options

A. 4T
B. 8T
C. 2T
D. 16T

Answer

B

Explanation

`implies T prop r^(3/2)`
`:. T_2/T_1 = ((r_2)/r_1)^(3//2) = ((4r)/r)^(3/2) =(4)^(3/2) = 2^3 = 8`
`:. T_(2) = 8T " " [ :. T_1 = T]`