Time Dilation - GRE Subject Test: Physics

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Question

At one point in time, two twins are 30 years old. At this time, one of them gets on a rocket and travels at 0.8 c, for what he experiences to be 12 years. How old is the twin that remained on Earth when the traveling twin returns home?

Answer

The equation for time dilation is given by:

$T'=\frac{T}{\sqrt{1-\frac{v^2}{c^2}}}$

In this problem v=0.8c T=12. Using this equation, we get:

$T'=\frac{12}{\sqrt{1-(\frac{4}{5})^2}}=\frac{12}{\sqrt{1-\frac{16}{25}}}=\frac{12}{\sqrt{\frac{9}{25}}} =\frac{12}{\frac{3}{5}}=(12)(\frac{5}{3})=20$

Adding 20 years to the age initial age of 30:

The Earth-twin is now 50.

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