The dimensional formula for a physical quanti | vedclass

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(D) Given the dimensional formula for $x$ is $x = M^{-1} L^{3} T^{-2}$.The formula for the maximum percentage error in $x$ is given by the propagation

Vedclass · Accepted Answer

$19$

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(D) Given the dimensional formula for $x$ is $x = M^{-1} L^{3} T^{-2}$.The formula for the maximum percentage error in $x$ is given by the propagation of errors rule:$\frac{\Delta x}{x} 	imes 100 = |(-1)| \frac{\Delta M}{M} 	imes 100 + |3| \frac{\Delta L}{L} 	imes 100 + |(-2)| \frac{\Delta T}{T} 	imes 100$.Substituting the given percentage errors for $M, L$ and $T$:$\frac{\Delta x}{x} 	imes 100 = 1(2\%) + 3(3\%) + 2(4\%)$.Calculating the values:$= 2\% + 9\% + 8\% = 19\%$.Therefore,the maximum percentage error in $x$ is $19\%$.

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 of error that occurs in measuring the quantity $x$ is (in $\%$)

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