In the density measurement of a cube, the mass and edge length are mea

1.	In the density measurement of a cube, the mass and edge length are measured as (10.00±0.10) kg and (0.10±0.01)m, respectively. The error in the measurement of density is:(A) 0.10 kg/m³ (B) 0.31 kg/m³(C) 0.07 kg/m³ (D) 0.01 kg/m³
Answer» Given : In the density measurement of a cube, the MASS and EDGE length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01)m, respectively. To find : The error in the measurement of density. solution : we know, volume of cube = (edge length)³ so, density of cube = mass of cube/volume of cube ⇒d = m/V = m/a³ To find error, formula will be ... ∆d/d = ∆m/m + 3∆a/a ......(1) here mass of cube = (10.00 ± 0.10) kg so, m = 10, ∆m = 0.1 edge length of cube = (0.1 ± 0.01) m so, a = 0.1 , ∆a = 0.01 now find error in the density using EQ (1). ∆d/10⁴ = 0.1/10 + 3 × 0.01/0.1 ⇒∆d/d = (0.01 + 3 × 0.1) = 0.31 kg/m³ Therefore the error in the measurement of density is 0.31 kg/m³. Therefore option (B) is correct CHOICE.

In the density measurement of a cube, the mass and edge length are measured as (10.00±0.10) kg and (0.10±0.01)m, respectively. The error in the measurement of density is:(A) 0.10 kg/m³ (B) 0.31 kg/m³(C) 0.07 kg/m³ (D) 0.01 kg/m³

Answer»

Given : In the density measurement of a cube, the MASS and EDGE length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01)m, respectively.

To find : The error in the measurement of density.

solution : we know, volume of cube = (edge length)³

so, density of cube = mass of cube/volume of cube

⇒d = m/V = m/a³

To find error, formula will be ...

∆d/d = ∆m/m + 3∆a/a ......(1)

here mass of cube = (10.00 ± 0.10) kg

so, m = 10, ∆m = 0.1

edge length of cube = (0.1 ± 0.01) m

so, a = 0.1 , ∆a = 0.01

now find error in the density using EQ (1).

∆d/10⁴ = 0.1/10 + 3 × 0.01/0.1

⇒∆d/d = (0.01 + 3 × 0.1) = 0.31 kg/m³

Therefore the error in the measurement of density is 0.31 kg/m³.

Therefore option (B) is correct CHOICE.