The percentage error in measuring $\mathrm{M}, \mathrm{L}$ and $\mathrm{T}$ are $1 \%, 1.5 \%$ and $3 \%$…

The percentage error in measuring $\mathrm{M}, \mathrm{L}$ and $\mathrm{T}$ are $1 \%, 1.5 \%$ and $3 \%$ respectively. Then the percentage error in measuring the physical quantity with dimensions $\mathrm{ML}^{-1} \mathrm{~T}^{-1}$ is
  1. $1 \%$
  2. $3.5 \%$
  3. $3 \%$
  4. $5.5 \%$

Solution

$\quad$ Let $\mathrm{X}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$
Then, $\frac{\Delta \mathrm{X}}{\mathrm{X}} \times 100=\left(\frac{\Delta \mathrm{M}}{\mathrm{M}}+\frac{\Delta \mathrm{L}}{\mathrm{L}}+\frac{\Delta \mathrm{T}}{\mathrm{T}}\right) \times 100$
As we know, $\frac{\Delta \mathrm{M}}{\mathrm{M}}=1 \%, \frac{\Delta \mathrm{L}}{\mathrm{L}}=1.5 \%$ and $\frac{\Delta \mathrm{T}}{\mathrm{T}}=3 \%$
$=(1+1.5+3) \%=5.5 \%$ ^

Asked in: JEE Mains - Units and Dimensions - Test 1

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