Answer to Question #171173 in Classical Mechanics for Marvelous

Question

) A metal cylinder has a length of 4 cm and diameter 2 cm. What percent uncertainty is introduced into the calculated circumference by an uncertainty of 0.01 cm in the diameter measurement? What percent uncertainty does this introduce in the calculated volume?

Answer 1

Given,

Length of the metal cylinder $(l)=4cm$

Diameter $(d)=2cm$

Uncertainty in the measurement of circumference = 0.01cm

percentage uncertainty in the measurement of volume(V)=?

$\frac{\Delta V}{V}\times 100 =\frac{2\Delta r}{r}\times 100 + \frac{\Delta l}{l}\times 100$

$=\frac{0.01\times 2\times 100}{1}+\frac{4\times 0.01\times 100}{4}$

$=2+1 = 3\%$

Hence, the required change in volume be 3%.