Question

If the length of a cylinder is l=(4.00+-0.001) cm radius r=(0.0250+-0.001) cm and mass m=(6.25+-0.01) gm .Calculate the percentage error in the determination of density ?

Answer 1

Answer:

The answer is 8.185 % .

Explanation:

Length of cylinder , l = (4.00 ± 0.001) cm

Radius of base of cylinder , r = (0.025 ± 0.001) cm

Mass of cylinder, m = (6.25 ± 0.01) gm

We know density  d = m/v

Volume of cylinder , v = πr²l

So, density , d = m/(πr²l)

Then fractional error can be written as,

∆d/d = ∆m/m + 2 × ∆r/r + ∆l/l

Given Data:

∆m = 0.01g , m = 6.25 g , ∆r = 0.001, r = 0.025 , ∆l = 0.001 and l = 4.00

Thus, ∆d/d = (0.01)/(6.25) + 2 × (0.001)/(0.025) + (0.001)/(4.00)

= 0.0016 + 0.08 + 0.00025

= 0.08185

Percentage error of density = 100 × fractional error of density

= 100 × 0.08185

= 8.185 %