Question

The accuracy in the measurement of speed of light measured as $3.00 \times {10^8}\;{\rm{m/s}}$ is:
A. 30%
B. $\dfrac{1}{3}\% $
C. 3%
D. $\dfrac{1}{{30}}\% $

Answer 1

Hint: We can use the concept and the expressions related with the accuracy and precisions. In expression we have used the least value up to which the measurement can be performed, so that we get the correct answer from the given options.

Complete step by step solution:
Given:
The speed of the light is \[3.00 \times {10^8}\;{\rm{m/s}}\]

The expression for the accuracy of the measurement of speed of light is,
\[a\% = \dfrac{{{\text{least value up to which speed of light can be measured}}}}{{\;{\rm{measured}}\;{\text{speed of light}}}} \times 100\]
Substitute the values in the above expression
$\begin{array}{l}
a\% = \dfrac{{0.01 \times {{10}^8}\;{\rm{m/s}}}}{{3 \times {{10}^8}\;{\rm{m/s}}}} \times 100\\
a\% = \dfrac{1}{3}\%
\end{array}$

Therefore, the option (B) is the correct answer that is $\dfrac{1}{3}\% $.

Note: Remember that, generally we calculate the answers of the problems that are related to percentage in decimal form. But here, the given options in the question are a whole number or in fraction, so do not calculate the answer in the decimal form.