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A space probe has an 18.0 m length when measured at rest. What length does an observer at rest measures when the probe is going by at a speed of 0.700 c?


1. 25.2 m
2. 12.9 m
3. 12.6 m
4. 9.18 m

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Correct Answer - Option 2 : 12.9 m

According to special theory of relativity,

\({L_{shortening}} = \frac{{{L_{Proper}}}}{\gamma }\)

Where \(\gamma = \frac{1}{{\sqrt {1 - {{\left( {\frac{V}{C}} \right)}^2}} }} = \frac{1}{{\sqrt {1 - {{\left( {\frac{{0.7C}}{C}} \right)}^2}} }}\)

\(\gamma = \frac{1}{{\sqrt {1 - 0.49} }} = \frac{1}{{\sqrt {0.51} }} = 1.40\)

\({L_{Shortening}} = \frac{{18.0}}{{1.40}} = 12.86\;m \approx 12.9\;m\)

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