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Units and Measurements question

2018 · Shift 0 · Q67
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Units and Measurements question

2018 · Shift 0 · Q67

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:
  1. A
    6%
  2. B
    2.5%
  3. C
    3.5%
  4. D
    4.5%
View written solutionFree

Correct answer: D

  1. Write the formula for density

For a cube of side length lll and mass mmm,

ρ=ml3\rho = \frac{m}{l^3}ρ=l3m​
  1. Use error propagation for products/powers

For maximum relative error:

Δρρ=Δmm+3Δll\frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + 3\frac{\Delta l}{l}ρΔρ​=mΔm​+3lΔl​

because the power of lll is 333.

  1. Substitute the given relative errors

Mass error =1.5%= 1.5\%=1.5%

Length error =1%= 1\%=1%

So,

Δρρ=1.5%+3(1%)\frac{\Delta \rho}{\rho} = 1.5\% + 3(1\%)ρΔρ​=1.5%+3(1%) Δρρ=1.5%+3%=4.5%\frac{\Delta \rho}{\rho} = 1.5\% + 3\% = 4.5\%ρΔρ​=1.5%+3%=4.5%
  1. Match with the options
4.5%\boxed{4.5\%}4.5%​

So the correct option is D.

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