Question

A force F is applied onto a square plate of side L. If the percentage error in determining L is $2%$ and that in F is $4%$, the permissible percentage error in determining the pressure is
(a) $2%$
(b) $4%$
(c) $6%$
(d) $8%$
(e) $1%$

Answer 1

Hint:In order to calculate the percentage error, we need to follow the formula of the error in this question which is percent error = [experimental value - theoretical value] / theoretical value x 100%.
Now, From the question,
Side of square plate $=L$
Percentage error in$L$ $=2%$
Percentage error in $F$$=4%$

We know that,
\[P=\dfrac{F}{A}=\dfrac{F}{{{L}^{2}}}\],
$\dfrac{\Delta P}{P}\times 100=\dfrac{\Delta F}{F}\times 100+2\dfrac{\Delta L}{L}\times 100$
$=\left[ 4+2\left( 2 \right) \right]%=8%$

Therefore, the correct answer for this question is option (d).

Additional Information: The purpose of a percent error calculation is to gauge how close a measured value is to a true value.Percent error (percentage error) is the difference between an experimental and theoretical value, divided by the theoretical value, multiplied by 100 to give a percent.In some fields, percent error is always expressed as a positive number. In others, it is correct to have either a positive or negative value. The sign may be kept to determine whether recorded values consistently fall above or below expected values.Percent error is one type of error calculation. Absolute and relative error are two other common calculations. Percent error is part of a comprehensive error analysis.

Note:While solving this question, we need to be careful with the formula of finding the error percentage as it is used in a modified way. This question can also be solved by different ways as per the convenience.