83. In the laboratory, the life time of a particle moving with velocity
2.8 x 10 m/s is found to be 2.5 x 10-7s, its proper life time is:
(a) 3.6 x 10
(b) 9.0 x10-8
(0) 3.6 X10-7
(d) 9.8 x 10-7
Answers
Answer:
The proper life time of the particle is 8.97\times10^{-8}\ sec8.97×10
−8
sec
Explanation:
Given that,
Speed of particle v=2.8\times10^{8}\ m/sv=2.8×10
8
m/s
Time t= 2.5\times10^{-7}\ sect=2.5×10
−7
sec
We need to calculate the proper life time of the particle
Using formula of proper time
t'=\dfrac{t_{0}}{\sqrt{1-(\dfrac{v}{c})^2}}t
′
=
1−(
c
v
)
2
t
0
Where, v = speed of the particle
c = speed of light
t' = observer time
Put the value into the formula
2.5\times10^{-7}=\dfrac{t_{0}}{\sqrt{1-(\dfrac{2.8\times10^{8}}{3\times10^{8}})^2}}2.5×10
−7
=
1−(
3×10
8
2.8×10
8
)
2
t
0
t_{0}=2.5\times10^{-7}\times\sqrt{1-(\dfrac{2.8\times10^{8}}{3\times10^{8}})^2}t
0
=2.5×10
−7
×
1−(
3×10
8
2.8×10
8
)
2
t_{0}=8.97\times10^{-8}\ sect
0
=8.97×10
−8
sec
Hence, The proper life time of the particle is 8.97\times10^{-8}\ sec8.97×10
−8
sec
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