The length of a uniform rod is 100.0 ,cm and | vedclass

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

Question

(A) The volume of a cylinder is given by $V = \pi r^2 l$.The relative error in volume is given by $\frac{\Delta V}{V} = 2 \frac{\Delta r}{r} + \frac{\

Vedclass · Accepted Answer

$2.1$

Vedclass · Answer

(A) The volume of a cylinder is given by $V = \pi r^2 l$.The relative error in volume is given by $\frac{\Delta V}{V} = 2 \frac{\Delta r}{r} + \frac{\Delta l}{l}$.Given values:Length $l = 100.0 \,cm = 1000 \,mm$,$\Delta l = 1 \,mm$.Radius $r = 1.00 \,cm = 10.0 \,mm$,$\Delta r = 0.1 \,mm$.Substituting these values into the error formula:$\frac{\Delta V}{V} = 2 	imes \left( \frac{0.1}{10.0} ight) + \left( \frac{1}{1000} ight)$.$\frac{\Delta V}{V} = 2 	imes (0.01) + 0.001 = 0.02 + 0.001 = 0.021$.The percentage error is $\frac{\Delta V}{V} 	imes 100 = 0.021 	imes 100 = 2.1 \%$.Therefore,the correct option is $A$.

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 ............. $\%$

Similar Questions

If the length of a cylinder is $l = (4.00 \pm 0.01) \; cm$,radius $r = (0.250 \pm 0.001) \; cm$,and mass $m = 6.25 \pm 0.01 \; g$,calculate the percentage error in the determination of density.

If the absolute error is $0.05 \ m$ for a measured length of $5 \ m$,what is the percentage error (in $\%$)?

If the radius of a sphere is $(5.3 \pm 0.1) \; cm$,then the percentage error in its volume will be:

What is the fractional error in $g$ calculated from $T = 2\pi \sqrt {l/g}$? Given fractional errors in $T$ and $l$ are $\pm x$ and $\pm y$ respectively?

Thickness of a pencil measured by using a screw gauge (least count $0.001 \,cm$) comes out to be $0.802 \,cm$. The percentage error in the measurement is ........... $\%$

Vedclass Test Series

Exam Paper Generator

Online Exam Module