Question

There are atomic (Cesium) clocks capable of measuring time with an accuracy of 1 part in ${10^{11}}$.If two such clocks are operated to precision,then after running for 5000 years,these will record a difference of
(A)1 day
(B)1 s
(C) ${10^{11}}$ s
(D)1 year

Answer 1

Hint: Here we will calculate the time difference of the clocks operated with the given accuracy of 1 part in ${10^{11}}$.We will calculate it for five thousand years and then convert it into s.We will then convert it into significant figures to get the desired answer.

Complete step by step answer: We have been the measuring time of the cesium clocks with an accuracy of 1 part in ${10^{11}}$.So $\Delta t \to \dfrac{1}{{{{10}^{11}}}}$
So, for five thousand years the time difference can be written as $\Delta t \to \dfrac{1}{{{{10}^{11}}}} \times 5000$ as the accuracy is one part in ${10^{11}}$.
The above time difference can be written as $\dfrac{{5000 \times 365 \times 24 \times 60 \times 60}}{{{{10}^{11}}}} \approx 1s$
So, these clocks after running for five thousand years will record a time difference of one second.

Hence the correct solution is option B

Additional information: The atomic clocks telling the time are quite precise and they often miss one tenth part of a second over the entire lifetime of the universe. Also, these clocks have use in astronomy, time telling etc.

Note: The conversion of the time difference to second should be properly done so as to get the desired answer. Also, the correct interpretation of the fact of the accuracy should be done correctly.