Concept explainers
(a)
Reading of clock in tail of rocket.
(a)
Explanation of Solution
Given:
Rocket has proper length
Rocket has one clock in nose and one in tail that are synchronized in frame of rocket.
Clock in nose of rocket and clock on ground both read zero as they pass each other.
Formula used:
Write the expression of time measured by clock in tail in frame of rocket
Here,
Write the expression of length of rocket according to ground frame
Here,
Substitute
Simplify the above expression
Calculation:
Substitute
Conclusion:
Thus, the clock in tail of rocket reads
(b)
Reading of clock in tail of rocket with respect to ground.
(b)
Explanation of Solution
Given:
Rocket has proper length
Rocket has one clock in nose and one in tail that are synchronized in frame of rocket.
Clock in nose of rocket and clock on ground both read zero as they pass each other.
Formula used:
Write the expression of time measured by clock in tail of rocket according to ground frame
Calculation:
Substitute
Conclusion:
Thus, the clock in tail of rocket reads
(c)
Reading of clock in nose of rocket according to ground.
(c)
Explanation of Solution
Given:
Rocket has proper length
Rocket has one clock in nose and one in tail that are synchronized in frame of rocket.
Clock in nose of rocket and clock on ground both read zero as they pass each other.
Formula used:
Write the expression of time measured by clock in nose of rocket in ground frame
Calculation:
Substitute
Conclusion:
Thus, the clock in nose of rocket reads
(d)
Reading of clock in nose with respect to frame of rocket.
(d)
Explanation of Solution
Given:
Rocket has proper length
Rocket has one clock in nose and one in tail that are synchronized in frame of rocket.
Clock in nose of rocket and clock on ground both read zero as they pass each other.
Formula used:
Since the clock in nose of rocket is synchronized with clock in tail of rocket in frame of rocket therefore
Here,
Calculation:
Substitute
Conclusion:
Thus, the clock in nose of rocket reads
(e)
Reading of clock on ground when signal is received by observer on ground.
(e)
Explanation of Solution
Given:
Rocket has proper length
Rocket has one clock in nose and one in tail that are synchronized in frame of rocket.
Clock in nose of rocket and clock on ground both read zero as they pass each other.
Signal is sent from nose of rocket to ground when clock in nose of rocket reads
Formula used:
Write the expression of time
Here,
Write the expression of time when signal is sent
Here,
Write the expression of the traveling time
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the clock on ground reads
(f)
Reading of clock in nose of rocket when signal is received at nose of rocket.
(f)
Explanation of Solution
Given:
Rocket has proper length
Rocket has one clock in nose and one in tail that are synchronized in frame of rocket.
Clock in nose of rocket and clock on ground both read zero as they pass each other.
Observer on ground sends return signal to nose of rocket upon reception of the signal.
Formula used:
Write the expression of time
Substitute
Write the expression of total time
Write the expression of time dilatation equation
Here,
Substitute
Calculation:
Substitute
Conclusion:
Thus, the clock in nose of rocket reads
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Chapter 39 Solutions
Physics For Scientists And Engineers
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