Question

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%. The maximum percentage error that occurs in measuring the quantity $X$ is :

• A. 19%
• B. 9%
• C. 17%
• D. 21%

Answer 1

The correct option is A 19%

$\left[X\right]=\left[M^{-1}{L}^3{T}^{-2}\right]$

$\Rightarrow Error=(\frac{△M}{M}+3\frac{△L}{L}+2\frac{△T}{T})$

$\Rightarrow 2+3\times \left(3\right)+2\times \left(4\right)$

$\Rightarrow$ 19 %