
(a)
The time difference between two neutrinos to cover the distance.
(a)

Explanation of Solution
Introduction:
Neutrinos travel at the speed nearly equal to the
Write the expression for time taken by first neutrino.
Here,
Write the expression for time taken by second neutrino.
Here,
Write the expression for time difference.
Substitute
Since, the speed of neutrino is nearly equal to the speed of light; therefore,
Substitute
Here,
Conclusion:
Thus, the time difference between two neutrinos to cover the distance is
(b)
The ratio of speed of neutrino to the speed of light.
(b)

Explanation of Solution
Introduction:
Neutrinos travel at the speed nearly equal to the speed of light. Time required is the distance covered by an object travelling with some speed.
Write the expression for theory of relativity.
Here,
Rearrange the above expression in terms of
Expand the above expression through binomial expansion.
Conclusion:
Thus, the ratio of speed of neutrino to the speed of light is
(c)
The speed difference and time difference between two neutrinos.
(c)

Explanation of Solution
Given:
The distance of supernova is
The energy of first neutrino is
The energy of first neutrino is
The mass of neutrino is
Formula used:
Write the expression for theory of relativity.
Here,
Rearrange the above expression in terms of
Expand the above expression through binomial expansion.
Write the expression for speed difference.
Here,
Simplify the above expression.
Write the expression for time taken by first neutrino.
Here,
Write the expression for time taken by second neutrino.
Here,
Write the expression for time difference.
Substitute
Since, the speed of neutrino is nearly equal to the speed of light; therefore,
Substitute
Here,
Calculation:
Substitute
Substitute
Conclusion:
The speed difference between two neutrinos is
(c)
The speed difference and time difference between two neutrinos.
(c)

Explanation of Solution
Given:
The distance of supernova is
The energy of first neutrino is
The energy of first neutrino is
The mass of neutrino is
Formula used:
Write the expression for theory of relativity.
Here,
Rearrange the above expression in terms of
Expand the above expression through binomial expansion.
Write the expression for speed difference.
Here,
Simplify the above expression.
Write the expression for time taken by first neutrino.
Here,
Write the expression for time taken by second neutrino.
Here,
Write the expression for time difference.
Substitute
Since, the speed of neutrino is nearly equal to the speed of light; therefore,
Substitute
Here,
Calculation:
Substitute
Substitute
Conclusion:
The speed difference between two neutrinos is
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Chapter 41 Solutions
Physics for Scientists and Engineers
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