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

The correct option is D $8$%

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