Question

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these reading in correct significant figure is.

• A. 4.623 s
• B. 4.62 s
• C. 4.6 s
• D. 5 s

Answer 1

The Correct Option is C

Sum of the numbers, considering the correct significant figures:

\[ \text{Sum} = 4.6 + 4.6 + 4.632 + 4.64 = 18.4 \]

The arithmetic mean is:

\[ \text{Arithmetic Mean} = \frac{\text{Sum}}{\text{Number of Observations}} = \frac{18.4}{4} = 4.6 \, s \]

The result is rounded to the correct significant figure.

Answer 2

Step 1: Write down the given readings
The four time period readings are:
4.62 s, 4.632 s, 4.6 s, and 4.64 s.

Step 2: Compute the arithmetic mean
\[ \text{Mean} = \frac{4.62 + 4.632 + 4.6 + 4.64}{4} \] \[ = \frac{18.492}{4} = 4.623 \, \text{s}. \]

Step 3: Apply the rule of significant figures
When calculating the mean, the result should not have more precision than the least precise measurement among the data. The least precise reading is 4.6 s, which has only two significant figures (one decimal place).

Step 4: Round off the mean to match the least precise measurement
The calculated mean = 4.623 s → rounded to one decimal place = 4.6 s.

Final answer

4.6 s