Correct Answer - Option 2 : Less than the age of P
Concept:
- According to Einstein's special theory of relativity, the measurement of the time interval of the two events will be different for different observers who are in relative motion. The difference in the elapsed time as measured by two clocks called time dilation.
- The time dilation formula is given as:
\(T=\frac{{{T}_{0}}}{\sqrt{1-{{\left( \frac{v}{c} \right)}^{2}}}}\)..(i)
Where,
- T = Time interval in the moving frame.
- T0 = Time interval in the rest frame.
- c = (\(3\times {{10}^{8}}\text{ m/s}\)) velocity of light in vacuum or free space
- v = velocity of the moving frame.
So, This theory predicts that time will slow down for an object moving at a very high speed with respect to some stationary reference frame.
Calculation:
According to P, the time taken by Q in the round trip is
\({{t}_{1}}=\frac{20c}{0.99c}=20.2yrs\)
Therefore according to Q his own age as Q completes the journey = (20 + 20.2) yrs = 40.2 yrs
Now,
According to P, the time taken by Q in the round trip is given by
\({{t}_{2}}=20\times \sqrt{1-\frac{{{v}^{2}}}{{{c}^{2}}}}=20\times \sqrt{{{\left( 1-0.99 \right)}^{2}}}=2.8yrs\)
Thus according to Q, his own age after completes the journey = (20 + 2.8)yrs = 22.8 yrs
Therefore the age of Q after the journey will be less than that of P. The result of this problem is actually a twin paradox of the special theory of relativity.
