Question

4 In an experiment, on determination of density of a metal given in the form of a
small cylindrical rod, the following observations are recorded.
i. Mass of cylinder = (6.7 +_0.1)g
ii. Radius of cylinder = (0.287 +_0.001)cm
iii. Length of cylinder = (3.28+_ 0.01)cm
Find percentage error in measurement of density.
a. 1.4%
b. 2.4%
d. 5%
C. 3%​

Answer 1

The percentage error in the measurement of density is 2.4 %.

In an experiment, on determination of density of a metal given in the form of a

small cylindrical rod, the following observations are recorded.

i. Mass of cylinder = (6.7 ± 0.1)g

ii. Radius of cylinder = (0.287 ± 0.001)cm

iii. Length of cylinder = (3.28 ± 0.01)cm

We have to find the percentage error in the measurement of density.

first find percentage error of mass, radius and length of cylinder.

∵ percentage error = error/theoretical value × 100

• % error of mass = 0.1/6.7 × 100 = 1.4 %
• % error of radius = 0.001/0.287 × 100 ≈ 0.34
• % error of length = 0.01/3.28 × 100 ≈ 0.30%

we know,

density = mass/volume

here volume of cylinder = πr²h

so, density of cylinder , ρ = m/πr²h

∴ % error of ρ = % error of m + 2 × % error of r + % error of h

⇒% error of ρ = 1.4 % + 2 × 0.34 % + 0.30 %

⇒% error of ρ = 2.38 % ≈ 2.4 %

Therefore the percentage error in the measurement of density is 2.4 %. option (B) is correct choice.