the time period of a pendulum is 2.0 s in a stationary inertial frame of reference. Its period measured by an observer moving at a speed of 0.6c with respect to the inertial frame of reference will be?
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# Answer- 2.5 s
# Explanation-
# Given-
Initial period Ti=2s
Speed of observer v=0.6c
# Solution-
Consider Tf be period measured by observer
Tf=γTi
By Einsteins theory of relativity
γ=1/√[1-(v/c)^2]
γ=1/√[1-(0.6)^2]
γ=1/√(1-0.36)
γ=1/√0.64
γ=1/0.8
γ=1.25
Now,
Tf=γTi
Tf=1.25×2
Tf=2.5s
Period of pendulum measured by observer is 2.5s.
# Explanation-
# Given-
Initial period Ti=2s
Speed of observer v=0.6c
# Solution-
Consider Tf be period measured by observer
Tf=γTi
By Einsteins theory of relativity
γ=1/√[1-(v/c)^2]
γ=1/√[1-(0.6)^2]
γ=1/√(1-0.36)
γ=1/√0.64
γ=1/0.8
γ=1.25
Now,
Tf=γTi
Tf=1.25×2
Tf=2.5s
Period of pendulum measured by observer is 2.5s.
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