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Found in: Page 1029

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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# What is γ? (a) if v=$${\bf{0}}.{\bf{250c}}$$? (b) If v=$${\bf{0}}.{\bf{500c}}$$

The Relativistic factor γ is

(a) γ=$$1.033$$

(b) γ=$$1.155$$

See the step by step solution

## Step 1: Formula for Relativistic factor, γ

The relativistic factor,

$$\gamma = \frac{1}{{\sqrt {1 - {{\left( {\frac{v}{c}} \right)}^2}} }}$$

Where v is the velocity relative to an observer and c= $${\rm{3}}{\rm{.00}}$$ X $${10^8}$$ $${\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}$$

## Step 2: To find the Relativistic factor, γ for v=$${\bf{0}}.{\bf{250}}$$c

(a) Here given that the velocity relative to an observer is, v=0.250 c

\begin{align}\gamma &= \frac{1}{{\sqrt {1 - {{\left( {\frac{v}{c}} \right)}^2}} }}\\ &= \frac{1}{{\sqrt {1 - {{\left( {\frac{{0.250c}}{c}} \right)}^2}} }}\\ &= \frac{1}{{\sqrt {1 - {{(0.250)}^2}} }}\\ &= \frac{1}{{\sqrt {1 - 0.0625} }}\\ &= 1.033\end{align}

Hence, the relativistic factor is 1.033.

## Step 3: To find the Relativistic factor, γ for v=$${\bf{0}}.{\bf{500}}$$c

(b)Here given that the velocity relative to an observer is, v=$$0.500$$c

\begin{align}\gamma &= \frac{1}{{\sqrt {1 - {{\left( {\frac{v}{c}} \right)}^2}} }}\\ &= \frac{1}{{\sqrt {1 - {{\left( {\frac{{0.500c}}{c}} \right)}^2}} }}\\ &= \frac{1}{{\sqrt {1 - {{(0.500)}^2}} }}\\ &= 1.155\end{align}

Hence, the relativistic factor is 1.155.

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