Question

At what speed relative to a laboratory does a clock tick at one quarter the rate of an identical clock at rest in the laboratory? Give your answer as a fraction of c.

Answer 1

let v is the speed of another closk with respect to laboratory.

use time dialation equation

t = t'/sqrt(1 - (v/c)^2)

==> t' = t*sqrt(1 - (v/c)^2)

given t' = t/4

t/4 = t*sqrt(1 - (v/c)^2)

1/4 = sqrt(1 - (v/c)^2)

1/16 = 1 - (v/c)^2

(v/c)^2 = 1 - 1/16

v/c = sqrt(15/16)

v = 0.968*c <<<<<<<<<---------------Answer