Question

The mass and density of a solid sphere are measured to be (12.4 +-0.1)kg and (4.6 +- 0.2) kg//m^3. Calculate the volume of the sphere with error limits .

Answer 1

Hence the volume of the sphere with error limits is V ± ΔV = (2.7 ± 0.14 ) m^3

Explanation:

Here, m ± Δm = (12.4 ± 0.1) kg

and ρ ± Δρ = (4.6 ± 0.2) kg / m^3

Volume V = m / ρ = 12.4 / 4.6

=2.69 m^3 = 2.7 m^3

Now, ΔV / V = ±(Δm / m + Δρ / ρ)

or ΔV = ± (Δm / m + Δρ / ρ) × V

= ± (0.1 / 12.4 + 0.2 / 4.6) × 2.7 = ± 0.14  

∴V ± ΔV = (2.7 ± 0.14 ) m^3

Hence the volume of the sphere with error limits is V ± ΔV = (2.7 ± 0.14 ) m^3