Two simple pendulums have time period `T` and `5T//4`. They start vibrating at the same instant from the mean position in the same phase. The phase difference (in rad) between them when the smaller pendulum completes one oscillation will be

Options

A. `(pi)/(6)`
B. `(pi)/(4)`
C. `(pi)/(3)`
D. `(pi)/(2)`

Answer

D

Explanation

Phase difference is `phi=omega_(S)t-omega_(l)t`
`thereforephi=(2pi)/(T)xx(5T)/(4)-(2pi)/(((5T)/(4)))xx(5T)/(4)`
or `phi=2pi((5)/(4)-1)`
or `phi=2pixx(1)/(4)=(pi)/(2)`