1. Tardigrade
  2. Question
  3. Physics
  4. The dimensional formula for a physical quantity x is [M-1L3T-2]. The errors in measuring the quantities M, L, and T, respectively, are 2 %, 3 %, and 4 %. What is the maximum percentage of error that occurs in measuring the quantity x?

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

Physical World, Units and Measurements

Solution:

$X =M^{-1} L^{3} T^{-2}$
$\frac{\Delta X}{X} =\frac{\Delta M}{M} +3\frac {\Delta L}{L} +2 \frac{\Delta T}{T}$
$=2+3\times 3+2 \times 4=19$