A physical quantity X is given by X = frac{2 | vedclass

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(C) The formula for the physical quantity is $X = \frac{2 k^3 \ell^2}{m \sqrt{n}}$.To find the relative error,we use the formula: $\frac{\Delta X}{X}

Vedclass · Accepted Answer

$12$

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(C) The formula for the physical quantity is $X = \frac{2 k^3 \ell^2}{m \sqrt{n}}$.To find the relative error,we use the formula: $\frac{\Delta X}{X} = 3 \frac{\Delta k}{k} + 2 \frac{\Delta \ell}{\ell} + \frac{\Delta m}{m} + \frac{1}{2} \frac{\Delta n}{n}$.Given percentage errors are $\frac{\Delta k}{k} 	imes 100 = 1\%$,$\frac{\Delta \ell}{\ell} 	imes 100 = 2\%$,$\frac{\Delta m}{m} 	imes 100 = 3\%$,and $\frac{\Delta n}{n} 	imes 100 = 4\%$.Substituting these values into the error equation:$\frac{\Delta X}{X} 	imes 100 = 3(1\%) + 2(2\%) + 3\% + \frac{1}{2}(4\%)$.$\frac{\Delta X}{X} 	imes 100 = 3\% + 4\% + 3\% + 2\% = 12\%$.Therefore,the percentage uncertainty in $X$ is $12\%$.

$A$ physical quantity $X$ is given by $X = \frac{2 k^3 \ell^2}{m \sqrt{n}}$. The percentage errors in the measurement of $k, \ell, m,$ and $n$ are $1\%, 2\%, 3\%,$ and $4\%$ respectively. The percentage uncertainty in the value of $X$ is: (in $\%$)

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