The mean length of an object is \(5~\text{cm}\). Which of the following measurements is most accurate?
1. \(4.9~\text{cm}\)
2. \(4.805~\text{cm}\)
3. \(5.25~\text{cm}\)
4. \(5.4~\text{cm}\)
Step 1: Find the difference between the measured values and the true value.
Given length \(l= 5~\text{cm}\)
Now, checking the errors with each option one by one, we get:
\(\Delta l_1 = 5-4.9= 0.1~\text{cm}\)
\(\Delta l_2 = 5-4.805= 0.195~\text{cm}\)
\(\Delta l_3 = 5.25-5= 0.25~\text{cm}\)
\(\Delta l_4 = 5.4-5= 0.4~\text{cm}\)
Step 2: Find the most accurate value.
Error \(\Delta l_1\)
Therefore, \(4.9~\text{cm}\) is the most precise.
Hence, option (1) is the correct answer.
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