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Chapter 6: Q51P (page 1250)

Two atomic clocks are carefully synchronized. One remains in New York, and the other is loaded on an airliner that travels at an average speed of and then returns to New York. When the plane returns, the elapsed time on the clock that stayed behind is . By how much will the readings of the two clocks differ, and which clock will show the shorter elapsed time? (Hint: Since u<<c , you can simplify1-u2/c2 by a binomial expansion.)

Short Answer

Expert verified

The difference of two clock times is鈭�t=鈭�t0=5脳10-9s .

Step by step solution

01

Definition of Speed

The term speed may be defined as the ratio of distance and time.

02

Determine the time difference of two clocks

For determine the time difference of two clocks the relation can be used here

鈭�t=鈭�t01-u2c2

Here鈭�t,鈭�t0,u are the time interval measured in the second frame of reference, the proper time in the rest frame and speed of the second frame with respect to rest frame respectively.

鈭�t=4h鈭�t=3600脳4s鈭�t=14400s

Now put the value in above result than

鈭�t0=鈭�t1-u2c2

is so small so

1-u2c2=1-u2c21/21-u2c21/2鈮�1-1u22c2

Therefore

鈭�t0=鈭�t1-u2c2鈭�t0=鈭�t1-u2c2鈭�t0=鈭�t-1u22c2鈭�t

Put all values than

鈭�t-鈭�t0=1u22c2鈭�t=1250223脳1082脳14400=5脳10-9s

Hence, the difference of two clock times is鈭�t-鈭�t0=5脳10-9s .

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Most popular questions from this chapter

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