3. A clock keep the correct time. With what speed should it move relative to the observer so that it may seem to lose 4 min in 24 hour?
Answers
Given: A clock keep the correct time.
To find: With what speed should it move relative to the observer?
Solution:
- Now, according to the question, it is related to time dilation.
- Time dilation states that it is a phenomenon in which a moving clock runs slow.
- The relation between time interval t of an event in a rest frame and the time interval of the same event in the frame of clock t1 is
t1 = (gama) (t)
where gama = 1 / √1-v²/c², v = speed of clock and c is speed of light.
- As we have given that the clock looses 4 minute in 24 hours, so
t = 24 x 3600 seconds = 86400 seconds
t1 = 24 x 3600 seconds - 4(60) seconds = 86160 seconds
- So from time dilation equation, we get:
86400 seconds = { 1 / √1-v²/c² } x 86160 seconds
√1-v²/c² = 86160 / 86400
1-v²/c² = 0.99722² = 0.99444
v²/c² = 1 - 0.99444 = 0.00556
v²/c² = 5.56 x 10 ^-3
v/c = √ 5.56 x 10 ^-3
v = 7.456 x 10^-2 x c = 7.456 x 10^-2 x 3 x 10^8
v = 22.368 x 10^6 m/s
Answer:
It should move at the speed of 22.368 x 10^6 m/s.