$A$ body travels uniformly a distance of $(13.8 \pm 0.2) \text{ m}$ in a time $(4.0 \pm 0.3) \text{ s}$. Its velocity with error limits and percentage error is

  • A
    $(4.0 \pm 0.31) \text{ m/s}, \pm 8\%$
  • B
    $(3.5 \pm 0.31) \text{ m/s}, \pm 9\%$
  • C
    $(5.0 \pm 0.37) \text{ m/s}, \pm 9\%$
  • D
    $(3.8 \pm 0.34) \text{ m/s}, \pm 7\%$

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$A$ projectile is thrown with velocity $U = 20 \ m/s \pm 5\%$ at an angle $60^{\circ}.$ If the projectile falls back on the ground at the same level,then which of the following values in $m$ cannot be a possible answer for the range?

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In an experiment,four quantities $p, q, r$,and $s$ are measured with percentage errors of $3 \%, 2 \%, 3 \%$,and $1 \%$ respectively. Quantity $A$ is calculated as follows: $A = \frac{pq^2}{r^2 s^4}$. The percentage error in $A$ is: (in $\%$)

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 numbers of oscillations. The observations are shown in the table. Least count for length $= 0.1 \text{ cm}$. Least count for time $= 0.1 \text{ s}$.
StudentLength $(cm)$Oscillations $(n)$Total Time $(s)$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 $E_{I}$,$E_{II}$,and $E_{III}$ are the percentage errors in $g$,i.e.,$(\frac{\Delta g}{g} \times 100)$ for students $I$,$II$,and $III$ respectively,which of the following is correct?

What is error in measurement? What is mistake in measurement?

Two resistors of resistances $R_1 = (100 \pm 3) \,\Omega$ and $R_2 = (200 \pm 4) \,\Omega$ are connected in series. The maximum absolute error and percentage error in the equivalent resistance of the series combination are:

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