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JEE Main
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Physics
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Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

An experiment is conducted to determine the density of a...

An experiment is conducted to determine the density of a cylindrical wire. The percentage errors in the measurement of mass, radius, and length of the wire are 2%2\%, 1.5%1.5\%, and 1%1\%, respectively. The maximum percentage error in the calculated density of the wire is

Options

  1. A4.5%4.5\%
  2. B6%6\%
  3. C2%2\%
  4. D5.25%5.25\%

Correct answer

B. 6%6\%

Step-by-step solution

The density ρ\rho of a cylindrical wire is given by ρ=Mπr2L\rho = \dfrac{M}{\pi r^2 L}, where MM is mass, rr is radius, and LL is length.

The maximum percentage error in density is given by:
Δρρ×100=ΔMM×100+2(Δrr×100)+ΔLL×100\dfrac{\Delta \rho}{\rho} \times 100 = \dfrac{\Delta M}{M} \times 100 + 2\left(\dfrac{\Delta r}{r} \times 100\right) + \dfrac{\Delta L}{L} \times 100

Substituting the given values:
Δρρ×100=2%+2(1.5%)+1%\dfrac{\Delta \rho}{\rho} \times 100 = 2\% + 2(1.5\%) + 1\%
Δρρ×100=2%+3%+1%=6%\dfrac{\Delta \rho}{\rho} \times 100 = 2\% + 3\% + 1\% = 6\%

Answer: 6%6\%
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