A clock is moving along the x axis at 0.6c.It reads zero as it passes the origin (x = 0).When it passes the x = 180 m mark on the x axis the clock reads:
A)0.60 $\mu$s
B)0.80 $\mu$s
C)1.00 $\mu$s
D)1.25 $\mu$s
E)1.67 $\mu$s

Question

Quizplus · Accepted Answer

The time dilation formula is given by:
$$t_0=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}$$
where $t$ is the time measured by the clock when it is moving at velocity $v$ with respect to an observer at rest and $t_0$ is the time measured by the observer at rest.

Here, $v=0.6c$, $t_0=0$ when the clock passes the origin, and $t$ is the time measured by the clock when it passes the mark at $x=180$ m.

Using distance-time relation, we have:
$$t=\frac{180\,	ext{m}}{v}=\frac{180\,	ext{m}}{0.6c}=\frac{180\,	ext{m}}{0.6	imes 3	imes 10^8\,	ext{m/s}}=1\,	ext{µs}$$

Substituting these values in the time dilation formula, we get:
$$t_0=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{1\,	ext{µs}}{\sqrt{1-\left(\frac{0.6c}{c}ight)^2}}=2.29\,	ext{µs}$$

Therefore, the clock reads $2.29\,	ext{µs}$ when it passes the $x=180$ m mark. However, we need to be careful with the significant figures. The answer has only two significant figures, since $180\,	ext{m}$ has only two significant figures. Therefore, we round off the answer to two decimal places, which gives:
$$t_0=2.29\,	ext{µs} \approx 2.3\,	ext{µs}$$

As per the given choices, the closest option is (B) 0.80 µs.

A Clock Is Moving Along the X Axis at 0 μ\muμ

A Clock Is Moving Along the X Axis at 0 $\mu$