Question

Imagine that a relativistic train travels past your lecture room at a speed of 0.894 c. The passengers of the train claim that when they measure the length of the train using standard meter bars found on the train, the length comes out to be 90.6 m. What would be the length of the train in the frame of the lecture room, if you measured it?

Answer 1

Answer:

The length of the train in the frame of the lecture room is 40.59 m.

Explanation:

Given that,

Speed = 0.894 c

Original length = 90.6 m

We need to calculate the length of the train in the frame of the lecture room

Using formula of length contraction

$L=L_{0}\sqrt{1-(\dfrac{v}{c})^2}$

Where, $L_{0}$=original length

v = speed of train

Put the value into the formula

$L=90.6\sqrt{1-(\dfrac{0.894c}{c})^2}$

$L=90.6\sqrt{1-0.894^2}$

$L=40.59\ m$

Hence, The length of the train in the frame of the lecture room is 40.59 m.