The period of oscillation of a simple pendulum in the experiment is recorded as $2.63\, s, 2.56 s, 2.42\, s, 2.71\, s$ and $2.80 \,s$ respectively. The average absolute error is ......... $s$
$0.1$
$0.11$
$0.01$
$1.0$
What is the fractional error in $g$ calculated from $T = 2\pi \sqrt {l/g} $ ? Given fraction errors in $T$ and $l$ are $ \pm x$ and $ \pm y$ respectively?
The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4\%$ and $3\%$ respectively, the maximum error in the measurement of density will be ........ $\%$
Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.
Student No. | Length of pendulum $(cm)$ | No. of oscillations $(n)$ | Total time for oscillations | Time period $(s)$ |
$1.$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
$2.$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
$3.$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
(Least count of length $=0.1 \,{m}$, least count for time $=0.1\, {s}$ )
If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $'g'$ for students $1,2$ and $3$ respectively, then the minimum percentage error is obtained by student no. ....... .
If the length of a cylinder is $l=(4.00 \pm 0.01) cm$, radius $r =(0.250 \pm 0.001) \;cm$ and mass $m =6.25 \pm 0.01\; g$. Calculate the percentage error in determination of density.
A public park, in the form of a square, has an area of $(100 \pm 0.2) m ^2$. The side of park is ......... $m$