Dimensional formula for a physical quantity x is left[ M ^{-1} L ^{3} T ^{-2}right] . errors in meas

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1.Units, Dimensions and Measurement

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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

A

$9$

B

$10$

C

$14$

D

$19$

Solution

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

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

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

$ = 19\% $

Standard 11

Physics

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