A spaceship travels at v = 0.6c relative to Earth — JEE Physics
A spaceship travels at $v = 0.6c$ relative to Earth. A clock on the spaceship ticks for $\tau_0 = 10$ s (proper time). Find the time elapsed on Earth (time dilation).
1 Answer
SJShruti Jain
✓ Accepted
· 1mo ago
▲ 16
$$\gamma = \frac{1}{\sqrt{1-v^2/c^2}} = \frac{1}{\sqrt{1-0.36}} = \frac{1}{\sqrt{0.64}} = \frac{1}{0.8} = 1.25$$
$$\Delta t = \gamma \tau_0 = 1.25 \times 10 = 12.5 s$$
More time elapses on Earth — confirming the moving clock runs slow.
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Discussion (2)
KS
Brilliant explanation, the substitution step is what I kept missing.
IM
Plotting it roughly also helps you sanity-check the sign.