The values of a number of quantities are used in a mathematical formula. The quantity that should be most precise and accurate in measurement is the one

  • A
    Having smallest magnitude
  • B
    Having largest magnitude
  • C
    Used in the numerator
  • D
    Used in the denominator

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$A$ physical quantity $x$ is related as $x = \frac{\sqrt{a}b^3}{c^4d^{-4}}$. Relative errors in the quantities $a, b, c$ and $d$ are $2\%, 1\%, 3\%$ and $4\%$ respectively. The relative error in $x$ will be: (in $\%$)

Can error be completely eliminated?

The period of oscillation of a simple pendulum is $T = 2 \pi \sqrt{L / g}$. The measured value of $L$ is $20.0 \; cm$ known to $1 \; mm$ accuracy,and the time for $100$ oscillations of the pendulum is found to be $90 \; s$ using a wrist watch of $1 \; s$ resolution. What is the accuracy in the determination of $g$ in $\%$?

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In an experiment, the coefficient of viscosity (in $mPa \cdot s$) of a liquid was determined as $2.62, 2.68, 2.58, 2.57, 2.54$ and $2.55$. The mean absolute error in the determination of the coefficient of viscosity of the liquid is

$A$ wire has a mass $0.3 \pm 0.003 \text{ g}$,radius $0.5 \pm 0.005 \text{ mm}$ and length $6 \pm 0.06 \text{ cm}$. The maximum percentage error in the measurement of its density is (in $\%$)

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