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

• A. $9$
• B. $10$
• C. $14$
• D. $19$

Answer 1

Answer: (D)

$19$

$X=\frac{m^3}{{Kgs}^2}=\frac{L^3}{{mT}^2}$

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

Percentage error $=[2+3\left(3\right)+2\left(4\right)]$%

Percentage error $=19$%