Question

A 2.99-m-long2.99-m-long rod, as measured in its rest frame, speeds by you longitudinally at 6.49×107 m/s6.49×107 m/s . You measure its length as it passes. By how many millimeters do you determine the rod has contracted?

Answer 1

Answer:

The contraction in the rod is 71 mm.

Explanation:

Given that,

original length L'= 2.99 m

Speed $v= 6.49\times10^{7}\ m/s$

We need to calculate the length

Using expression for length contraction

$L'=\gamma L$

$L=\dfrac{L'}{\gamma}$

Where,

$\gamma=\dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}$

$L=\sqrt{1-\dfrac{v^2}{c^2}}L'$

Where, v = speed of observer

c = speed of the light

Put the value into the formula

$L=\sqrt{1-\dfrac{(6.49\times10^{7})^2}{(3\times10^{8})^2}}\times2.99$

$L=2.919\ m$

The expression for the contraction in the rod

$d =L'-L$

$d=2.99-2.919$

$d=0.071$

$d= 71\ mm$

Hence, The contraction in the rod is 71 mm.