The dimensional formula for a physical quantity x is [ M ^ -1 L ^… - Vidyadip

Question

The dimensional formula for a physical quantity $x$ is $\left[ M ^{-1} L ^{3} T ^{-2}\right]$. The errors in measuring the quantities $M , L$ and $T$ respectively are $2 \%, 3 \%$ and $4 \%$. The maximum percentage of error that occurs in measuring the quantity $x$ is

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Answer

$\,x\,\, = \,\,{M^{ - 1}}{L^3}{T^{ - 2}}$

$\frac{{\Delta x}}{x} \times 100 = \frac{{\Delta M}}{M} \times 100 + \frac{{3\Delta L}}{L} \times 100 + \frac{{2\Delta T}}{T} \times 100\,$

$ = 2\% + 3 \times 3\% + 2 \times 4\% = 2\% + 9\% + 8\% \,\,$

$ = 19\% $

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