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(A) Given the physical quantity $X = M^a L^b T^c$.According to the theory of errors,if a quantity $X$ is related to measured quantities $M, L,$ and $T

Vedclass · Accepted Answer

$a\alpha + b\beta + c\gamma$

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(A) Given the physical quantity $X = M^a L^b T^c$.According to the theory of errors,if a quantity $X$ is related to measured quantities $M, L,$ and $T$ by the relation $X = M^a L^b T^c$,the relative error in $X$ is given by $\frac{\Delta X}{X} = a \left( \frac{\Delta M}{M} ight) + b \left( \frac{\Delta L}{L} ight) + c \left( \frac{\Delta T}{T} ight)$.To find the maximum percentage error,we consider the absolute values of the coefficients.The percentage error in $X$ is given by $\frac{\Delta X}{X} 	imes 100 = a \left( \frac{\Delta M}{M} 	imes 100 ight) + b \left( \frac{\Delta L}{L} 	imes 100 ight) + c \left( \frac{\Delta T}{T} 	imes 100 ight)$.Substituting the given percentage errors $\alpha, \beta,$ and $\gamma$ for $M, L,$ and $T$ respectively,we get:Maximum percentage error in $X = a\alpha + b\beta + c\gamma$.

$A$ physical quantity is given by $X = M^a L^b T^c$. The percentage errors in the measurement of $M, L,$ and $T$ are $\alpha, \beta,$ and $\gamma$ respectively. The maximum percentage error in the quantity $X$ is:

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