Question

Synchronized clocks are stationed at regular intervals, a million apart, along a straight line. When the clock next to you reads 12 noon:

(a) What time do you see on the ${90}^{th}$clock down the line?

(b) What time do you observe on that clock?

Short answer

(a) The time on clock down the line is 11:55 A.M.

(b) The time observed by you on ${90}^{\mathrm{th}}$clock is 12 noon.

Step-by-step solution

Given information: 

Given data:

The distance between two adjacent clocks is 1 million km .

Determine the time on 90thclock down:

(a)

Write the relation between distance, speed, and time.

$\mathit{t}\mathbf{=}\frac{\mathbf{d}}{\mathbf{c}}$ …… (1)

Here, d is the distance, and c is the speed of light $\left(3\times {10}^{8}m/s\right)$.

Calculate the distance between${90}^{\mathrm{th}}$clock and the next clock.

$$\begin{gathered} \mathrm{d}=90\times \left(1\mathrm{million}\mathrm{km}\times \frac{{10}^9\mathrm{m}}{1\mathrm{million}\mathrm{km}}\right) \\ \mathrm{d}=90\times {10}^9\mathrm{m} \end{gathered}$$

Substitute the value of d and c in the above relation.

$$\begin{gathered} t=\frac{\left(90\times {10}^9\mathrm{m}\right)}{\left(3\times {10}^8\mathrm{m}/\mathrm{s}\right)} \\ t=300\mathrm{s}\times \left(\frac{1\min }{60\mathrm{s}}\right) \\ \mathrm{t}=5\min \\ \mathrm{As}\mathrm{the}\mathrm{time}\mathrm{is}5\min \mathrm{less}\mathrm{than}12\mathrm{noon},\mathrm{the}{90}^{\mathrm{th}}\mathrm{clock}\mathrm{down}\mathrm{will}\mathrm{read} \\ 11:55\mathrm{A}.\mathrm{M}.. \\ \mathrm{Therefore},\mathrm{the}\mathrm{time}\mathrm{on}{90}^{\mathrm{th}}\mathrm{clock}\mathrm{down}\mathrm{the}\mathrm{line}\mathrm{is}11:55\mathrm{A}.\mathrm{M}. \end{gathered}$$

Determine the time observed by you on 90thclock down:

(b)

Since, 12 noon is observed on the clock.

Therefore, the time observed by you on${90}^{\mathrm{th}}$ clock is$12\mathrm{noon}$.