Answer :
Explanation:
It is given that,
Life time of a pion, [tex]t=26\ ns=26\times 10^{-9}\ s[/tex]
Distance covered by a pion, d = 15 cm = 0.15 m
We need to find distance from the rest frame of the pion. Firstly, we can calculate the speed of the pion as :
[tex]v=\dfrac{d}{t}[/tex]
[tex]v=\dfrac{0.15}{26\times 10^{-9}}[/tex]
v = 5769230.76 m/s
or
[tex]v=5.76\times 10^6\ m/s[/tex]
Its length in the rest frame is given by the formula as :
[tex]d_o=d\sqrt{1-\dfrac{v^2}{c^2}}[/tex]
[tex]d_o=0.15\sqrt{1-\dfrac{(5.76\times 10^6)^2}{(3\times 10^8)^2}}[/tex]
[tex]d_o=0.149\ m[/tex]
or
[tex]d_o=14.9\ cm[/tex]
So, the length of the pion in rest frame is 14.9 cm. Hence, this is the required solution.