Question

The mean time period of a simple pendulum is 1.92 s. Mean absolute error in the time period is

0.05 s. To express the maximum estimate of error, the time period should be written as:

(a) T = (1.92 0.01)s

(b) T = (1.92 0.25)s

(c) T = (1.92 0.05)s

(d) T = (1.92 0.10)s​

Answer 1

answer : option (C) (1.92 ± 0.05)s

explanation : The mean time period of a simple pendulum , T = 1.92 s

and mean absolute error in the time period , ∆T = 0.05 s

then, To express maximum estimate of error, the time period should be written as T ± ∆T = (1.92 ± 0.05)s

[ note : if you get experimentally some of observations in time period $T_1,T_2,T_3,T_4,.....T_n$,

then, To express maximum estimate of error, first you should find out mean of given observations e.g., $T=\frac{\displaystyle\Sigma^{i=n}_{i=1}{T_i}}{n}$

and then, find $\Delta T_1=T-T_1$, $\Delta T_2=T-T_2$....an so on

in last find it mean absolute value e.g., ∆T = $\frac{|\Delta T_1|+|\Delta T_2|+...|\Delta T_n|}{n}$ this is what ?, of course mean absolute error of time period, T .and you should write it in (T ± ∆T) ]