Correct Answer - Option 3 : 6%
The correct answer is option 3) i.e. 6%
Concept:
The error of a product or a quotient: If two physical quantities A and B have measured values A ± ΔA, B ± ΔB respectively where ΔA and ΔB are their absolute errors, the possible error ΔZ in the operation Z = AB or Z = A ÷ B is given by:
\( \frac{\Delta Z}{ Z} = \frac{∆A}{A} + \frac{∆B}{B}\)
Calculation:
Let the side of a cube be 's'.
The volume of the cube, V = s3
Given that,
\(\frac{\Delta s}{s} = 2\% =0.02\)
On differentiating V w.r.t s,
\(\frac{\Delta V}{\Delta s} = 3s^2\)
\(\Rightarrow \Delta V= {3s^2}\times \Delta s\)
\(\Rightarrow \frac{\Delta V}{V} = \frac{3s^2}{s^3} \times\Delta s\)
\(\Rightarrow \frac{\Delta V}{V} = 3\times\frac{\Delta s}{s}\)
\(\Rightarrow \frac{\Delta V}{V} = 3\times 0.02 = 0.06 = 6\%\)
Combination of errors:
When physical quantities involving a mathematical operation have errors associated with them, there will be an error in the result arising from its combination.
1. The error of a sum or a difference: If two physical quantities A and B have measured values A ± ΔA, B ± ΔB respectively where ΔA and ΔB are their absolute errors, the possible error ΔZ in the operation Z = A ± B is given by:
± ΔZ = ± ΔA ± ΔB
2. The error in case of a measured quantity raised to a power:
If Z = Ax then
\(\frac{\Delta Z}{Z} = x\frac{\Delta A}{A}\)