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JEE Main 2018

JEE Main 2018 Physics question on Units and Measurements

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%
Show answer and solution

Correct option: D

Solution

Density ρ = M/L³, so the relative error in density is:

Δρ/ρ = ΔM/M + 3(ΔL/L) = 1.5% + 3(1%) = 1.5% + 3% = 4.5%

The factor of 3 comes from the cube of the length in the denominator, and errors add up for maximum error, giving 4.5%.

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