Question

A physical quantity is represented by the relation Y = M^aL^bT^-c. If the percentage errors in the measurement of M, L and T are respectively α%, β% and λ% respectively, then the total error will be –
1. (αa – βb + λc)%
2. (αa – βb - λc)%
3. (αa + βb + λc)%
4. (αa + βb - λc)%

Answer 1

Correct Answer - Option 3 : (αa + βb + λc)%
\(\begin{array}{l} \frac{{{\rm{\Delta }}Y}}{Y} \times 100\% = \left( {a\frac{{{\rm{\Delta }}M}}{M} \times 100 + b\frac{{{\rm{\Delta }}L}}{L} \times 100 + c\frac{{{\rm{\Delta }}T}}{T} \times 100} \right)\% \\ \frac{{{\rm{\Delta }}Y}}{Y} \times 100\% = \left( {\alpha b + \beta b + \gamma c} \right)\% \end{array}\)