Question

. A student measures the time period of 1$00$ oscillations of a simple pendulum four times The data set is $90s$, $91s$, $92s$ and 95s. If the minimum division in the measuring clock ' Is, then the reported mean time should be

• A. $(92\pm 2)s$
• B. $(92\pm 5)s$
• C. $(92\pm 1.8)s$
• D. $(92\pm 3)s$

Answer 1

Answer: (A)

$(92\pm 2)s$

$\begin{array}{c}\text{Given - Time Readings}\to \text{90s}91s,92s,95s\\ \text{Mean Reading}\overline{R}=\frac{90+91+92+95}{4}\end{array}$

$\overline{R}=92s.$

$\text{mean error}=\frac{|92-90|+|92-91|+|92-92|+|92-95|}{4}$ $=\frac{2+1+0+3}{4}=1.5$

$\begin{array}{c}\text{since least count of the clock is only}1sec\\ \text{Hence}\pm 1.5sec\text{must be reported}\pm 2\sec \\ \text{Hence Time}=92\pm 2\text{sec.}\end{array}$