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JEE Main
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Physics
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Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

The density of a solid cube is determined by measuring its mass and...

The density of a solid cube is determined by measuring its mass and its edge length. The measured mass is M=(40.0±0.4)M = (40.0 \pm 0.4) kg and the measured edge length is l=2.0l = 2.0 m. If the maximum percentage error in the calculated density is 7%7\%, what is the absolute error in the measurement of the edge length?

Options

  1. A0.120.12 m
  2. B2.02.0 m
  3. C0.0530.053 m
  4. D0.040.04 m

Correct answer

D. 0.040.04 m

Step-by-step solution

The density ρ\rho of a cube is given by ρ=Ml3\rho = \dfrac{M}{l^3}.

The maximum percentage error in density is given by:
Δρρ×100=(ΔMM×100)+3(Δll×100)\dfrac{\Delta \rho}{\rho} \times 100 = \left( \dfrac{\Delta M}{M} \times 100 \right) + 3 \left( \dfrac{\Delta l}{l} \times 100 \right)

First, calculate the percentage error in mass:
%ΔM=0.440.0×100=1%\% \Delta M = \dfrac{0.4}{40.0} \times 100 = 1\%

Substitute the known values into the error equation:
7%=1%+3(%Δl)7\% = 1\% + 3(\% \Delta l)
3(%Δl)=6%3(\% \Delta l) = 6\%
%Δl=2%\% \Delta l = 2\%

The percentage error in the edge length is 2%2\%. To find the absolute error Δl\Delta l:
Δll×100=2\dfrac{\Delta l}{l} \times 100 = 2
Δl2.0×100=2\dfrac{\Delta l}{2.0} \times 100 = 2
Δl=4.0100=0.04\Delta l = \dfrac{4.0}{100} = 0.04 m

Answer: 0.040.04 m
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