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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
The Special Theory of Relativity

Concepts Of Physics MCQ Edition [Volume 2] · Physics · The Special Theory of Relativity

If a person lives on average 100 years in his rest frame, determine...

If a person lives on average 100100 years in his rest frame, determine how long he lives in the earth frame if he spends his entire life on a spaceship travelling at 60%60\% of the speed of light.

Options

  1. A160160 years
  2. B125125 years
  3. C100100 years
  4. D8080 years

Correct answer

B. 125125 years

Step-by-step solution

The proper time interval, which is the lifetime measured in the person's rest frame, is Δt0=100\Delta t_0 = 100 years.

The velocity of the spaceship relative to the Earth frame is v=0.6cv = 0.6c.

Using the time dilation formula, the lifetime measured in the Earth frame is given by:

Δt=Δt01−v2c2\Delta t = \dfrac{\Delta t_0}{\sqrt{1 - \dfrac{v^2}{c^2}}}

Substituting the given values:

Δt=1001−(0.6)2\Delta t = \dfrac{100}{\sqrt{1 - (0.6)^2}}

Δt=1001−0.36\Delta t = \dfrac{100}{\sqrt{1 - 0.36}}

Δt=1000.64\Delta t = \dfrac{100}{\sqrt{0.64}}

Δt=1000.8=125 years\Delta t = \dfrac{100}{0.8} = 125 \text{ years}
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