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1. units,dimensions and measurement — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
In an experiment four quantities $a, b, c$ and $d $ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{{{a^3}{b^2}}}{{cd}}$. $ \%$ error in $P$ is ........ $\%$
  • ✓
    $14$
  • B
    $10$
  • C
    $7$
  • D
    $4$
✓

Answer

Correct option: A.
$14$
a
As, $P = \frac{{{a^3}{b^2}}}{{cd}}$
$ \% $, error, in, $P$, is
$\frac{{\Delta P}}{P} \times 100 = \left[ {3\left( {\frac{{\Delta a}}{a}} \right) + 2\left( {\frac{{\Delta b}}{b}} \right) + \frac{{\Delta c}}{c} + \frac{{\Delta d}}{d}} \right] \times 100$
$ = 3\left[ {3 \times 1\%  + 2 \times 2\%  + 3\%  + 4\% } \right] = 14\% $
 

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