Question

A student measures the time period of $100$ oscillations of a simple pendulum four times. That data set $90s,91s,95s$ and $92s$. If the minimum division in the measuring clock is $1s,$ then he reported time should be

• A. $92\pm 5.0s$
• B. $92\pm 2s$
• C. $92\pm 3s$
• D. $92=2s$

Answer 1

The correct option is B $92\pm 2s$

Time period of $100$ oscillations are $90s,91s,95s,92s,$

Mean value of time $=\frac{90+91+95+92}{4}$

$t_m=92s$

Absolute error,

$|\Delta t_1|=|t_m-t_1|=2s$

$|\Delta t_2|=|t_m-t_2|=1s$

$|\Delta t_3|=|t_m-t_3|=3s$

$|\Delta t_4|=|t_m-t_4|=0s$

Mean absolute error, $\Delta t_{mean}=\frac{2+1+3+0}{4}=1.5s\approx 2s$

So, mean time is $(92\pm 2s)$