The maximum percentage errors in the measurem | vedclass

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

Question

(B) The angular momentum $(J)$ of a ring about its geometrical axis is given by $J = I \omega$. Since the moment of inertia of a ring is $I = M R^2$,w

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) The angular momentum $(J)$ of a ring about its geometrical axis is given by $J = I \omega$. Since the moment of inertia of a ring is $I = M R^2$,we have $J = M R^2 \omega$. The relative error in $J$ is given by $\frac{\Delta J}{J} = \frac{\Delta M}{M} + 2 \frac{\Delta R}{R} + \frac{\Delta \omega}{\omega}$. To find the maximum percentage error,we multiply by $100$: $\frac{\Delta J}{J} 	imes 100 = \left( \frac{\Delta M}{M} 	imes 100 ight) + 2 \left( \frac{\Delta R}{R} 	imes 100 ight) + \left( \frac{\Delta \omega}{\omega} 	imes 100 ight)$. Given $\frac{\Delta M}{M} 	imes 100 = 2 \%$,$\frac{\Delta R}{R} 	imes 100 = 1 \%$,and $\frac{\Delta \omega}{\omega} 	imes 100 = 1 \%$. Substituting these values: $\frac{\Delta J}{J} 	imes 100 = 2 \% + 2(1 \%) + 1 \% = 2 \% + 2 \% + 1 \% = 5 \%$.

The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its angular momentum $(J = I \omega)$ about its geometrical axis. (in $\%$)

Similar Questions

$A$ body of mass $(5 \pm 0.5) \ kg$ is moving with a velocity of $(20 \pm 0.4) \ m/s$. Its kinetic energy will be

The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$,the percentage error in calculated volume of cylinder is ............. $\%$

$A$ physical quantity $A$ is related to four observables $a, b, c,$ and $d$ as follows: $A = \frac{a^2 b^3}{c \sqrt{d}}$. The percentage errors of measurement in $a, b, c,$ and $d$ are $1\%, 3\%, 2\%,$ and $2\%$ respectively. What is the percentage error in the quantity $A$?

What is least count? What is called least count error?

Vedclass Test Series

Exam Paper Generator

Online Exam Module