special relativity problems with answers

special relativity problems with answers

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1) The period of a pendulum is measured to be 3.0 sec in the inertial frame of the pendulum. what is the period of the pendulum when measured by observer moving at a speed of 0.95c with respect to the pendulum.

ans:

To=T*√(1-u²/c²)

where: To is the proper time, T is the relativistic time.

               3.0=T*√(1-0.95² )

              T=30.76 sec.

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2) A space ship is measured to be 100m long while it is at rest w.r.t an observer. If this spaceship now flies with speed of 0.99c, what length will the observer find for the spaceship?

ans:

X₂-X₁=100m

u=0.99c, t₂=t₁

X'₂ –X'₁=γ[(X₂-X₁)-u(t₂-t₁)]

Where γ=1/ √(1-u²/c²)=1/√(1-0.99²)=7.08

X'₂ –X'₁=7.08[(100)-0.99c(0)]=708.88m