A force F is applied on a square plate of length L . If the percentage error in the determination of L is 3 \% and in F is 4 \% , then permissible error in the calculation of pressure is

Correct answer: B. 10 \% Given, Percentage error in length =3 \% Percentage error in force =4 \% We know that, Pressure, P=(F)/(A) Area of square =(L)^2 aligned P & =(F)/(L^2) (Δ P)/(P) & =(Δ F)/(F)+(2 Δ L)/(L) ((Δ P)/(P) × 100) & =((Δ F)/(F) × 100)+2((Δ L)/(L) × 100) & =4 \%+2(3 \%)=10 \% aligned

JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

A force F is applied on a square plate of length L . If the...

A force

F

is applied on a square plate of length

L

. If the percentage error in the determination of

L

3 \%

and in

F

4 \%

, then permissible error in the calculation of pressure is

Options

A $13 \%$
B $10 \%$
C $7 \%$
D $12 \%$

Correct answer

B. $10 \%$

Step-by-step solution

Given, Percentage error in length

=3 \%

Percentage error in force

=4 \%

We know that, Pressure,

\quad P=\frac{F}{A}

Area of square

=(L)^2

\begin{aligned} P & =\frac{F}{L^2} \\ \frac{\Delta P}{P} & =\frac{\Delta F}{F}+\frac{2 \Delta L}{L} \\ \left(\frac{\Delta P}{P} \times 100\right) & =\left(\frac{\Delta F}{F} \times 100\right)+2\left(\frac{\Delta L}{L} \times 100\right) \\ & =4 \%+2(3 \%)=10 \% \end{aligned}

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