Question

A clock has uncertainty 1 x ${10}^{-8}$ in measuring a one second. The clock will need correction of 1 s after:

• A. 5.1709 years
• B. 3.1709 years
• C. 4.1709 years
• D. None of the above

Answer 1

The correct option is B 3.1709 years

$\text{Given -}\text{uncertainity in}1\text{sec}\Rightarrow 1\times {10}^{-8}\text{sec}$

$\text{Since a the least count of the clock is}1sec$

$\begin{array}{c}\text{for}1\text{second we get an errors of}1\times {10}^{-8}\text{sec}\\ \text{for}n\text{seconds we get an errors of}n\times {10}^{-8}\text{sec.}\end{array}$

$\begin{array}{c}\text{we need to find How many seconds contribute to}\\ \text{an error of}1sec\text{.}\\ \begin{array}{cc}\Rightarrow \text{error}& =n\times {10}^{-8}=1\\ & \Rightarrow n={10}^8\end{array}\end{array}$

$\begin{array}{c}\text{after}{10}^8\text{seconds we need to correct the clock again!}\\ \text{Time}={10}^8\text{seconds}=\frac{{10}^8}{3600\times 24\times 365}\text{years}\\ =3.17\text{years.}\end{array}$