It is claimed that two cesium clocks,if allowed to run for $100$ years,free from any disturbance,may differ by only about $0.02\; s$. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of $1\; s$?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The total time duration is $100$ years.
Converting this into seconds: $100 \times 365 \times 24 \times 60 \times 60 = 3.15 \times 10^{9} \; s$.
The total time difference between the two clocks over this duration is $0.02 \; s$.
To find the accuracy for a $1 \; s$ interval,we calculate the relative error or the precision per unit time.
The error per unit time is $\frac{0.02 \; s}{3.15 \times 10^{9} \; s} \approx 6.35 \times 10^{-12} \; s$.
This means that for every $1 \; s$ measured,the clock is accurate to within approximately $6 \times 10^{-12} \; s$.

Explore More

Similar Questions

The angle of $1^{\prime}$ (minute of arc) in radian is nearly equal to

How is time regulated in a wristwatch and a cesium clock?

The distance of the Sun from Earth is $1.5 \times 10^{11} \,m$ and its angular diameter is $2000 \,s$ when observed from the Earth. The diameter of the Sun will be ...........

Define astronomical unit,light year,and parsec.

In an experiment to estimate the size of a molecule of oleic acid,$1\, mL$ of oleic acid is dissolved in $19\, mL$ of alcohol. Then $1\, mL$ of this solution is diluted to $20\, mL$ by adding alcohol. Now,$1$ drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water,forming a one-molecule-thick layer. Lycopodium powder is sprinkled evenly over the film,and its diameter is measured. Knowing the volume of the drop and the area of the film,we can calculate the thickness of the film,which gives us the size of the oleic acid molecule.
Read the passage carefully and answer the following questions.
$(a)$ Why do we dissolve oleic acid in alcohol?
$(b)$ What is the role of lycopodium powder?
$(c)$ What would be the volume of oleic acid in each $mL$ of the solution prepared?
$(d)$ How will you calculate the volume of $n$ drops of this solution of oleic acid?
$(e)$ What will be the volume of oleic acid in one drop of this solution?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo