Time for $20$ oscillations of a pendulum is measured as $t_1 = 39.6\, s$,$t_2 = 39.9\, s$,and $t_3 = 39.5\, s$. What is the precision in the measurements? What is the accuracy of the measurement?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Given,$t_1 = 39.6\, s$,$t_2 = 39.9\, s$,and $t_3 = 39.5\, s$.
The least count of the measuring instrument is $0.1\, s$ (as measurements have only one significant figure after the decimal point).
Precision in the measurement $=$ Least count of the instrument $= 0.1\, s$.
The average time for $20$ oscillations is given by:
$t_{avg} = \frac{t_1 + t_2 + t_3}{3} = \frac{39.6 + 39.9 + 39.5}{3} = \frac{119.0}{3} = 39.666... \approx 39.7\, s$.
Absolute errors in the measurements are:
$\Delta t_1 = |t_{avg} - t_1| = |39.7 - 39.6| = 0.1\, s$
$\Delta t_2 = |t_{avg} - t_2| = |39.7 - 39.9| = 0.2\, s$
$\Delta t_3 = |t_{avg} - t_3| = |39.7 - 39.5| = 0.2\, s$
Average absolute error (Accuracy) $= \frac{\Delta t_1 + \Delta t_2 + \Delta t_3}{3} = \frac{0.1 + 0.2 + 0.2}{3} = \frac{0.5}{3} \approx 0.17\, s$.
Rounding off to one decimal place,the accuracy of the measurement is $\pm 0.2\, s$.

Explore More

Similar Questions

In the experiment of $Ohm's$ law,a potential difference of $5.0\, V$ is applied across the ends of a conductor of length $10.0\, cm$ and diameter of $5.00\, mm$. The measured current in the conductor is $2.00\, A$. The maximum permissible percentage error in the resistivity of the conductor is (in $\%$)

The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$,the percentage error in calculated volume of cylinder is ............. $\%$

$A$ particle covers a distance of $(13.8 \pm 0.2) \ m$ in $(4 \pm 0.3) \ s$. Its velocity under error limits will be

Difficult
View Solution

$A$ force '$F$' is applied on a square plate of side '$L$'. If the percentage error in determining '$L$' is $3\%$ and that in '$F$' is $2\%$, then the percentage error in determining the pressure is: (in $\%$)

$A$ current-carrying conductor obeys Ohm's law $(V = RI)$. If the current passing through the conductor is $I = (5 \pm 0.2) \text{ A}$ and the voltage developed is $V = (60 \pm 6) \text{ V}$, then find the percentage error in resistance $R$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo