A satellite is launched into a circular orbit of radius `R` around the earth. While a second is lunched into an orbit of radius `1.01R` The period of the second satellite is longer than the first one by approximately:

Options

A. `0.5%`
B. `1.0%`
C. `1.5%`
D. `3.0%`

Answer

C

Explanation

`(T_(2))/(T_(1)) = ((R_(2))/(R_(1)))^(3//2) = ((0.01R)/(R ))^(3//2) = (0.01)^(3//2)`
`= (1 + (1)/(100))^(3//2) = 1 + (3)/(2 xx 100)`
`%` change inn time period `= ((T_(2) - T_(1))/(T_(1))) xx 100`
`= ((T_(2))/(T_(1)) - 1) xx 100 = (3)/(200) xx 100 = 1.5%`