Question

A metre stick move along its length with a certain speed. The apparent length of the moving metre stick as measured by a stationary observer on the ground is found to be 98 cm. Then, the velocity of the meter stick in terms of the speed of light in vacuum c will be:
1. 0.17 c
2. 0.19 c
3. 0.98 c
4. 0.14 c

Answer 1

Correct Answer - Option 2 : 0.19 c

Concept:

If we measure the length of anything moving relative to our frame, we find its length L to be smaller than the proper length L₀ that would be measured if the object were stationary. 

At relativistic speeds, Close to the speed of light, distances measured are not the same when measured by different observers.

Length Contraction:

Length contraction is the decrease in the measured length of an object from its proper length when measured in a reference frame that is moving with respect to the object.

It is given by 

\(L = {L_{0}} \sqrt {1-{\frac{V^2}{C^2}}}\)

where L₀ is the length of the object in its rest frame, and L is the length in the frame moving with velocity V;

Calculation:

Given L = 98 cm; L₀ = 1m = 100 cm;

\(98 = {100} \sqrt {1-{\frac{V^2}{C^2}}}\)

V = 0.199 C