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 L_{0} 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 L_{0} 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; L_{0} = 1m = 100 cm;

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

**V = 0.199 C**