Clocks and their relative speeds

You're right, option D should also be correct. Sorry for the mistake. In summary, both options C and D are correct as the hour hand of the defective watch and the correct watch will be at the same position at 11 a.m. on March 2nd, 2012 or March 12th, 2012. This is because the defective watch gains 3 minutes every hour and will need 720/3 = 240 hours to gain 12 hours, which is the same amount of time added by the extra day in a leap year.
  • #1
mpx86
10
0

Homework Statement


A watch gains 3 minutes every hour. If it is set right at 11 a.m. on February 21st, 2012, when will the hour hand of this defective watch and a correct watch be at the same position?
A)
9 p.m. on February 21st, 2012
B)
11 p.m. on February 28th, 2012
C)
11 a.m. on March 2nd, 2012
D)
11 a.m. on March 12th, 2012

Homework Equations

The Attempt at a Solution


[/B]
If the defective and the correct watch show the same time, the defective watch will have gained 12 hours, i.e., 720 minutes. Since it gains 3 minutes every hour, it will need 720/3 = 240 hours to gain 12 hours. In other words, both watches will show the same time after 10 days. Counting from 11 a.m. on February 21St, 2012, both watches will show the same time at 11 a.m. on March 2nd, 2012.

However, the watches would show same time when the difference between them is 480 hours, so C and D should be both correct..(however the book states option C as the only correct answer)
 
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  • #2
Did you have to factor in that 2012 is a leap year and so February has an extra day?
 
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Likes mpx86
  • #3
Oops, silly me.
 

FAQ: Clocks and their relative speeds

How do clocks measure time?

Clocks measure time by using a consistent and precise mechanism, such as the oscillations of a pendulum or the vibrations of a quartz crystal, to track the passing of seconds, minutes, and hours.

Do all clocks keep the same time?

No, different clocks can keep different times due to factors such as their design, accuracy, and environment. However, all clocks should be able to display the same time at a given moment if they are synchronized.

How does the relative speed of a clock affect its time?

According to Einstein's theory of relativity, time is relative and can be affected by the speed at which an observer is moving. The faster a clock is moving, the slower it will appear to tick from the perspective of a stationary observer.

Can clocks in space keep time differently than clocks on Earth?

Yes, due to the effects of gravity and velocity in space, clocks can experience time dilation and keep time differently than clocks on Earth. This has been observed and tested by scientists using atomic clocks on satellites.

How do scientists measure the accuracy of a clock?

Scientists measure the accuracy of a clock by comparing it to a reference clock that is known to keep accurate time. This can be done using precision instruments and mathematical calculations to determine the percentage of error between the two clocks.

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