Question

a ray of light hits a piece of glass as shown

At what speed, in m/s, would a moving clock lose 2.1 ns in 1.0 day according to experimenters on the ground? Hint: Use the binomial approximation. Express your answer using two significant figures.

Answer 1

If the dilated time t' and that the original time be t then we must have,

1

v is the velocity with which the clock moves

The clock loses 2.1 ns and 1 day in terms of second is

1 day = 24 x 60 x 60 s = 86400 s

So, we must have,

86400 = 86400 - 2.1 × 10-9 " 를

22 86400 – 2.1 x 10-9 or, V1-2= 86400

or, 33 = 1 - 2.43 x 10-14

Expanding binomially and neglecting higher order terms we have

1- 5=1-2.43 x 10-14

or, 2=2.43 x 10-14

or, v = 2 x 2.43 x 10-14 x 3 x 108 m/s = 66.14 m/s

This is the required velocity