Question

A stick of $1m$ is moving with velocity of $2.7\times {10}^{8}m{s}^{-1}$. What is the apparent length of the stick $(c=3\times {10}^{8}m{s}^{-1})$

• A. $10m$
• B. $0,22m$
• C. $0.44m$
• D. $2.4m$

Answer 1

The correct option is C $0.44m$

Given,

$l_0=1m$

$v=2.7\times {10}^{8}m/s$

$c=3\times {10}^{8}m/s$

Length contraction in special theory of relativity.

$l=l_0\sqrt{1-\frac{v^2}{c^2}}$

$l=1\times \sqrt{1-\frac{2.7\times 2.7}{3\times 3}}$

$l=0.435m$