Four persons measure the length of a rod as $20.00 \ cm$, $19.75 \ cm$, $17.01 \ cm$, and $18.25 \ cm$. The relative error in the measurement of the average length of the rod is:

  • A
    $0.24$
  • B
    $0.18$
  • C
    $0.06$
  • D
    $0.08$

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$A$ certain body weighs $22.42 \; g$ and has a measured volume of $4.7 \; cc$. The possible errors in the measurement of mass and volume are $0.01 \; g$ and $0.1 \; cc$,respectively. Then the maximum percentage error in the density will be: (in $\%$)

Zero error belongs to the category of

If the maximum percentage error in the measurement of distance $(h)$ and time $(t)$ are '$e_1$' and '$e_2$' respectively,the percentage error in the measurement of acceleration of gravity $(g)$ is [use $h=\frac{1}{2} gt^2$].

In the measurement of a physical quantity $X = \frac{A^2 B}{C^{1/3} D^3}$, the percentage errors introduced in the measurements of the quantities $A, B, C$, and $D$ are $2 \%, 2 \%, 4 \%$, and $5 \%$, respectively. Then, the minimum amount of percentage error in the measurement of $X$ is contributed by:

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 $(s)$ 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 $= 0.1 \, cm$,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. ....... .

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