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Two particles approach each other with a speed 0.8 c with respect to the laboratory. Their relative speed is.
1. 0.912 c
2. 0.95 c
3. 0.975 c
4. 0.85 c

1 Answer

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Best answer
Correct Answer - Option 3 : 0.975 c

Correct option-3

Concept:

According to the second postulate of relativity (verified by extensive experimental observation) says that classical velocity addition does not apply to light.

On performing extensive experimental work physicists get an idea that either the light is an exception, or the classical velocity addition formula only works at low velocities. The correct formula for one-dimensional relativistic velocity addition is given by:

\(u=\frac{{{u}^{'}}+v}{1+\frac{{{u}^{'}}v}{{{c}^{2}}}}\)..(i)

where,

v = Relative velocity between two observers 

u = velocity of an object relative to one observer.

u' = velocity relative to the other observer.

(For ease of visualization, we often choose to measure u in our reference frame, while someone moving at v relative to us measures u′.)
vu′c2Calculation:

Given-

u' = 0.8c

c =\(3\times {{10}^{8}}m/s\) and 

v = 0.8c

On substituting the given values in the above equation (i), we get

\(u=\left( \frac{0.8c+0.8c}{1+\frac{0.64{{c}^{2}}}{{{c}^{2}}}} \right)m/s\)

    \(=\left( \frac{1.6}{1.64} \right)m/s\) \(=0.975\text{ }m/s\)

\(\therefore u=0.975\text{ }m/s\)

Hence, Option-3 is the correct answer.

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