Question

Beth and Charles are at rest relative to each other. Anjay runs past at velocity v while holding a long pole parallel to his motion. Anjay, Beth, and Charles each measure the length of the pole at the instant Anjay passes Beth. Rank in order, from largest to smallest, the three lengths LA, LB, and LC. Explain.

Anjay Beth Charles

Answer 1

Here,

In case of Anjay :

The pole is in motion with him,i.e, he's running with the pole itself.hence he'll be able to measure or observe the rest length of the pole (because,pole is in 'rest' relative to him!).

LA = L

In case of Beth and Charles :

They both are observering the motion of the system(Anjay with pole) from outside.

Its like observing length of train from the platform.

Length observed by Beth & Charles = L₀

Actual lenght of the pole = L_a

v = speed at which Anjay is running.

According to the principle of relativity -    $L_{0} = L_{a} \sqrt1 - v^{2}/c^{2}$

LB = LC = L₀

and;

LA > LB = LC.