The percentage error in measuring M, L and T are 1%, 1.5% and 3% respectively. Then the percentage error in measuring the physical quantity with dimensions $ML^{-1}T^{-1}$ is

Answer (5)

Given,

$\displaystyle \frac {\Delta M} {M}\times 100=1\%,\frac {\Delta L} {L}\times 100=1.5\%$

and $\displaystyle \frac {\Delta T} {T}\times 100=3\%$

Let, $X = ML^{-1}T^{-1}$

Then,

$\displaystyle \begin{aligned}\frac {\Delta X} {X}\times 100 &= \left(\frac {\Delta M} {M}+\frac {\Delta L} {L}+\frac {\Delta T} {T}\right)\times 100\\&=(1+1.5+3)\%=5.5\%\end{aligned}$