If error in measuring diameter of a circle is $4\%$, the error in circumference of the circle would be
$2$
$8$
$4$
$1$
Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.
They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length $=0.1 \mathrm{~cm}$
Least count for time $=0.1 \mathrm{~s}$
Student | Length of the pendulum $(cm)$ | Number of oscillations $(n)$ | Total time for $(n)$ oscillations $(s)$ | Time period $(s)$ |
$I.$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
$II.$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
$III.$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,
We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be $2.63 \;s , 2.56 \;s , 2.42\; s , 2.71 \;s$ and $2.80 \;s$. Calculate the absolute errors, relative error or percentage error.
In a experiment to measure the height of a bridge by dropping a stone into water underneath, if the error in the measurement of times is $0.1\;s$ at the end of $2\;s$, then the error in the estimation of the height of the bridge will be
Thickness of a pencil measured by using a screw gauge (least count $0.001 \,cm$ ) comes out to be $0.802 \,cm$. The percentage error in the measurement is ........... $\%$
If $x = a -b,$ then percentage error in $x$ will be