The pressure on a circular plate is measured | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The pressure $p$ on a circular plate is given by the formula $p = \frac{F}{A}$,where $F$ is the force and $A$ is the area of the plate. Since the

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(C) The pressure $p$ on a circular plate is given by the formula $p = \frac{F}{A}$,where $F$ is the force and $A$ is the area of the plate. Since the plate is circular,$A = \pi R^2$,where $R$ is the radius.Therefore,$p = \frac{F}{\pi R^2}$.Using the rules of propagation of errors,the relative error in $p$ is given by:$\frac{\Delta p}{p} = \frac{\Delta F}{F} + 2 \frac{\Delta R}{R}$.To find the percentage error,we multiply by $100$:$\frac{\Delta p}{p} 	imes 100 = \left( \frac{\Delta F}{F} 	imes 100 ight) + 2 \left( \frac{\Delta R}{R} 	imes 100 ight)$.Given that the percentage error in force $\frac{\Delta F}{F} 	imes 100 = 5 \%$ and the percentage error in radius $\frac{\Delta R}{R} 	imes 100 = 3 \%$,we substitute these values:$	ext{Percentage error in } p = 5 \% + 2(3 \%) = 5 \% + 6 \% = 11 \%$.Thus,the percentage error in the measurement of pressure is $11 \%$.

The pressure on a circular plate is measured by measuring the force on the plate and the radius of the plate. If the errors in measurement of the force and the radius are $5 \%$ and $3 \%$ respectively,the percentage of error in the measurement of pressure is (in $\%$)

Similar Questions

$A$ physical quantity $P$ is given by $P = \frac{A^3 B^{1/2}}{C^{-4} D^{3/2}}$. The quantity which brings in the maximum percentage error in $P$ is

Find the relative error in $Z$,if $Z = \frac{A^{4} B^{1/3}}{C D^{3/2}}$.

The percentage error in the measurement of $g$ is $.....\%$ (Given that $g = \frac{4 \pi^2 L}{T^2}$,$L = (10 \pm 0.1) \, cm$,$T = (100 \pm 1) \, s$)

$A$ physical quantity $x$ is calculated from the relation $x = \frac{a^2 b^3}{c \sqrt{d}}$. If the percentage errors in $a, b, c,$ and $d$ are $2\%, 1\%, 3\%,$ and $4\%$ respectively,what is the percentage error in $x$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module