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

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 %

Tardigrade Admin · Accepted Answer

Side of square plate =L Percentage error in L=2 % Percentage error in F=4 % We know that, P=(F/A)=(F/L2) (Δ P/P) × 100 =(Δ F/F) × 100+2 ⋅ (Δ L/L) × 100 =[4+2(2)] %=8 %

Q. 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

$2%$

$4%$

$6%$

$8%$

$1%$

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

Q. 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

2%

4%

6%

8%

1%

Side of square plate =L Percentage error in L=2% Percentage error in F=4% We know that, P=AF​=L2F​ PΔP​×100 =FΔF​×100+2⋅LΔL​×100 =[4+2(2)]%=8%