GATE 2026 PH – Question 35
A rocket of length 18.0 m is moving at speed 0.9c (where c is the speed of light) parallel to its own length, relative to the earth. The length of the rocket measured in meters by an observer on earth (rounded off to two decimal places) is _____
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Correct answer: 7.81 to 7.89
Explanation
**Length contraction:** an object of proper length $L_0$ moving at speed $v$ along its length is measured to have the length
$$L=L_0\sqrt{1-\frac{v^2}{c^2}}.$$
**Numbers.** $L_0=18.0$ m and $v=0.9c$:
$$L=18.0\sqrt{1-0.81}=18.0\sqrt{0.19}=18.0\times0.4359=\mathbf{7.85\ m}.$$