Tag: units and measurement: error analysis

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Questions Related to units and measurement: error analysis

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The mass of a beaker is found to be ($10.1 \pm 0.1)gm $ when empty and $(17.3 \pm 0.1)gm$ when partially filled with a liquid. What is the best value for the mass of the liquid together with the possible limits of accuracy?

  1. $(7.2  \pm 0.2)gm$

  2. $(7.2  \pm  0.1)gm$

  3. $(7.1  \pm  0.2)gm$

  4. $(7.2  \pm  0.3)gm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here mass of the liquid , $m=m _2-m _1=17.3-10.1=7.2 gm$

So the relative error, $\dfrac{\Delta m}{m}=\pm\left[\dfrac{\Delta m _1}{m _1}+\dfrac{\Delta m _2}{m _2}\right]$
or $\Delta m=\pm\left[\dfrac{\Delta m _1}{m _1}+\dfrac{\Delta m _2}{m _2}\right]\times m=\pm[0.1/10.1+0.1/17.3]\times 7.2=\pm 0.1 gm$
Thus mass of liquid with possible accuracy $=(7.2\pm 0.1) gm$

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Measure of two quantities along with the precision of respective measuring instrument is:
$A = 2.5 ms^{-1}\pm 0.5 ms^{-1}$
$B = 0.10s \pm 0.01 s$
The value of AB will be :

  1. $(0.25\pm 0.08)m$

  2. $(0.25\pm 0.5)m$

  3. $(0.25\pm 0.05)m$

  4. $(0.25\pm 0.135)m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given :  $\Delta A = 0.5 \ m/s$        $\Delta B = 0.01 \ s$

The absolute value of AB  $ = 2.5\times 0.10 = 0.25 \ m$

Relative error in AB,    $\dfrac{\Delta AB}{AB} = \dfrac{\Delta A}{A} +\dfrac{\Delta B}{B}$

$\therefore$   $\dfrac{\Delta AB}{0.25} = \dfrac{0.5}{2.5} +\dfrac{0.01}{0.10}$

$\implies \ \Delta AB = 0.075 = 0.08 \ m$
Thus value of AB is  $(0.25\pm0.08) \ m$

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

If accuracy of weighing machine is better than 1/2 percent, a student record his own mass. Choose the option that explains the recording most accurately.

  1. 6.43 kg

  2. 60 kg

  3. 64.3 kg

  4. 600kg

  5. 643 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This question is intended to assess your knowledge of realistic values for physical quantities as well as an understanding of experimental error and significant figures. Only 60 kg and 64.3 kg are likely masses for an adult human. When recording measurements, it is assumed that there is some measurement error in the last digit recorded. For both possible values for the student's weight, 1/2 percent is about 0.3 kg. Therefore, a mass recorded to better than this accuracy will indicate tenths of a kilogram.