Two simple pendulums have time periods `T` and `5T//4`. They start vibrating at the same instant from the mean position in the same phase. The phase difference between them when the pendulum with higher time period complets one oscillation is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

D

Explanation

`x_(1) = A_(1) sin ((2pi)/(T)t), x_(2) = A_(2) sin ((2pi)/((5T)/(4))t)`
At `t = (5T)/(4)`, phase of 1st oscilllator `= (2pi)/(T) (5T)/(4)=(5pi)/(2)`
Phase of 2nd oscillator `(2pi)/(((5T)/(4)))=(5T)/(4) = 2pi`
Phase difference `= (5pi)/(2) - 2pi = (pi)/(2) = 90^(@)`