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Units and Measurement question

2019 · Q153
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Units and Measurement question

2019 · Q153

NEETPhysicsUnits and MeasurementMCQ+4 / −1
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2 %, 3 %and 4 % respectively. Then the maximum percentage of error in the measurement X, where
X = A2B1/2C1/3D3{{{A^2}{B^{1/2}}} \over {{C^{1/3}}{D^3}}}C1/3D3A2B1/2​, will be :
  1. A
    16%
  2. B
    -10%
  3. C
    10%
  4. D
    (313)\left( {{3 \over {13}}} \right)(133​)%
View written solutionFree

Correct answer: A

Given,

X = A2B1/2C1/3D3{{{A^2}{B^{1/2}}} \over {{C^{1/3}}{D^3}}}C1/3D3A2B1/2​

ΔXX=2ΔAA+12ΔBB+13ΔCC+3ΔDD{{\Delta X} \over X} = {{2\Delta A} \over A} + {1 \over 2}{{\Delta B} \over B} + {1 \over 3}{{\Delta C} \over C} + 3{{\Delta D} \over D}XΔX​=A2ΔA​+21​BΔB​+31​CΔC​+3DΔD​

⇒\Rightarrow⇒ ΔXX×100=2(1%)+12(2%)+13(3%)+3(4%){{\Delta X} \over X} \times 100 = 2\left( {1\% } \right) + {1 \over 2}\left( {2\% } \right) + {1 \over 3}\left( {3\% } \right) + 3\left( {4\% } \right)XΔX​×100=2(1%)+21​(2%)+31​(3%)+3(4%) = 16 %

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