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

Answer: (D)

Side of square plate $=L$
Percentage error in $L=2 \%$
Percentage error in $F=4 \%$
We know that, $P=\frac{F}{A}=\frac{F}{L^{2}}$
$\frac{\Delta P}{P} \times 100$
$=\frac{\Delta F}{F} \times 100+2 \cdot \frac{\Delta L}{L} \times 100$
$=[4+2(2)] \%=8 \%$