How errors made in measuring variables in an experiment affect the final result

Question

How errors made in measuring variables in an experiment affect the final result is an important consideration in physics. Let us see how errors made in measuring the length and diameter of a cylinder affect the precision of the volume. In one set of measurements, suppose you make a 10% error in measuring the length of a cylinder but make no error in the diameter measurement. In another set of measurements, suppose you make a 10% error in the diameter measurement but make no error in the length measurement. Which set of measurements results in the largest percent error in the volume? support answer by numerical calculations.

Explanation / Answer

volume v=pi*R^2*L

error = dV/V = pi*2*(dR/R )*(dL/L)

a) error in measurement of length = dL/L = 10%

then error in volumre = pi*2*(dR/R )*10% = 10%

b) error in measurement of radius = dR/R= 10%

then error in volumre = pi*2*10%*(dl/L)= 2* 10% = 20%

so error in mw=easurin the diameter will result in larger percent error in the volume

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.