Question 70 of 121
A physical quantity is found to depend on quantities by the relation . The percentage error in and are and respectively. Then, the percentage error in is:
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Answer: (C)
Given quantity is .
The relative error in measuring is given by
Hence, the required percentage error is given by
\begin{matrix}\dfrac{\Delta Q}{Q}\times 100 & = & 4\left(\dfrac{\Delta a}{a}\times 100\right)+3\left(\dfrac{\Delta b}{b}\times 100\right)+2\left(\dfrac{\Delta c}{c}\times 100\right) \\ & = & 4\times 3%+3\times 4%+2\times 5% \\ & = & 12%+12%+10% \\ & = & 34%\end{matrix}
The relative error in measuring is given by
Hence, the required percentage error is given by
\begin{matrix}\dfrac{\Delta Q}{Q}\times 100 & = & 4\left(\dfrac{\Delta a}{a}\times 100\right)+3\left(\dfrac{\Delta b}{b}\times 100\right)+2\left(\dfrac{\Delta c}{c}\times 100\right) \\ & = & 4\times 3%+3\times 4%+2\times 5% \\ & = & 12%+12%+10% \\ & = & 34%\end{matrix}