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(D) The pressure $P$ on a square plate of side $l$ is given by $P = \frac{F}{A} = \frac{F}{l^2}$.Using the formula for the propagation of errors,the r

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$8$

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(D) The pressure $P$ on a square plate of side $l$ is given by $P = \frac{F}{A} = \frac{F}{l^2}$.Using the formula for the propagation of errors,the relative error in $P$ is given by $\frac{\Delta P}{P} = \frac{\Delta F}{F} + 2\frac{\Delta l}{l}$.To find the maximum percentage error,we multiply by $100$:$\left( \frac{\Delta P}{P} 	imes 100 ight)_{\max} = \left( \frac{\Delta F}{F} 	imes 100 ight) + 2 	imes \left( \frac{\Delta l}{l} 	imes 100 ight)$.Given that the percentage error in force $\frac{\Delta F}{F} 	imes 100 = 4\%$ and the percentage error in length $\frac{\Delta l}{l} 	imes 100 = 2\%$.Substituting these values,we get:$\left( \frac{\Delta P}{P} 	imes 100 ight)_{\max} = 4\% + 2 	imes 2\% = 4\% + 4\% = 8\%$.

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum percentage error in the measurement of force and length are respectively $4\%$ and $2\%$,the maximum percentage error in the measurement of pressure is ....... $\%$

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