An object is at rest in the Home Frame. Imagine an Other Frame moving at a speed of $|\beta|=\frac{4}{5}$ with respect to the Home Frame. The object's length in the Other Frame is measured to be $15 \mathrm{~ns}$. What is its length as observed in the Home Frame?
A) $15 \mathrm{~ns}$
B) $12 \mathrm{~ns}$
C) $9 \mathrm{~ns}$
D) $19 \mathrm{~ns}$
E) 25 ns
F) Other (specify)

Question

Quizplus · Accepted Answer

$$L_{R}=L / \sqrt{1-\beta^{2}}=L / \sqrt{1-\frac{16}{25}}=L / \sqrt{\frac{9}{25}}=\frac{5}{3}(15 \mathrm{~ns})=25 \mathrm{~ns} .$$

An Object Is at Rest in the Home Frame ∣β∣=45|\beta|=\frac{4}{5}∣β∣=54​ With Respect to the Home Frame

An Object Is at Rest in the Home Frame $|\beta|=\frac{4}{5}$ With Respect to the Home Frame