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Two simple pendulums of length l m and 16 m start at t =0 from mean position. The minimum time after which they will be again in phase will be

a
4T/3
b
4T
c
2T/3
d
T/3

detailed solution

Correct option is A

The phase of simple pendulum is given by θ=ωt where ω is angular speed.   Phase of first pendulum =ω1t  Phase of second pendulum =ω2t  Phase difference =2nπ ω1t−ω2t=2nπ or 2πTt−2π4Tt=2nπ ∵ω1=2π/T  and  ω2=2π/4T Puttirg n = 1, we get t1T−14T=1 or t34T=1 or t=4T3

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