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MHT CET · Physics · Mathematics in Physics

A physical quantity ' X ' is related to four measurable quantities ' a ', ' b ', ' c ' and ' d ' as \(\mathrm{X}=\mathrm{a}^2 \mathrm{~b}^3 \mathrm{c}^{5 / 2} \mathrm{~d}^{-2}\). The percentage error in the measurement of ' \(a\) ', ' \(b\) ', ' \(c\) ' and ' \(d\) ' are \(1 \%, 2 \%, 2 \%\) and \(4 \%\) respectively. The percentage error in measurement of quantity ' X ' is

  1. A \(15 \%\)
  2. B \(17 \%\)
  3. C \(21 \%\)
  4. D \(23 \%\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(21 \%\)

Step-by-step Solution

Detailed explanation

\(\frac{\Delta \mathrm{X}}{\mathrm{X}} \times 100\% = \left|2 \frac{\Delta \mathrm{a}}{\mathrm{a}}\right| \times 100\% + \left|3 \frac{\Delta \mathrm{b}}{\mathrm{b}}\right| \times 100\% + \left|\frac{5}{2} \frac{\Delta \mathrm{c}}{\mathrm{c}}\right| \times 100\% + \left|-2 \frac{\Delta \mathrm{d}}{\mathrm{d}}\right| \times 100\%\) \(= 2(1\%) + 3(2\%) + \frac{5}{2}(2\%) + 2(4\%)\)
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