Question

a) Explain and give a numerical example of time dilation.

b) Explain and give a numerical example of length contraction.

Answer 1

a) when an observer sitting in an inertial frame at rest, observes a clock in his frame then he observes the clock to be working normally. when the same clock is kept in another frame moving with respect to the observer, the clock is observed to be slowed down. this phenomena of time delay is called time dilation. this is observed only if the the second frame is moving with a velocity comparable to the speed of light. The dilated time is given as

where t' is time in moving frame
t is the time observed in the rest frame of observer
v is the velocity of moving frame
c is the velocity of light

consider a clock moving with speed 0.5c shows elapsed time to be 1s. the the time elapsed observed by a stationray observer will be

t=1.16s

b) when an observer sitting in an inertial frame at rest, measures a length in a frame moving with respect to the inertial frame of observer, the length is observed to be shorten. this called length contraction.

l' is the length in moving frame

l is the length in the rest frame

a rocket ship is 100m long on ground. when its in flight its length is 99m. what is the velocity og rocket?

l'=99m
l=100m

putting in above equation we get v=0.14c