In the measurement of a physical quantity $$X=A2BC1/3D3$$. The percentage errors introduced in the measurements of the quantities A, B, C and D are $$2$$%, $$2$$%, $$4$$% and $$5$$% respectively. Then the minimum amount of percentage of error in the measurement of X is contributed by:

Question

In the measurement of a physical quantity $$X=A2BC1/3D3$$. The percentage errors introduced in the measurements of the quantities A, B, C and D are $$2$$%, $$2$$%, $$4$$% and $$5$$% respectively. Then the minimum amount of percentage of error in the measurement of X is contributed by:

Infinity Learn · Accepted Answer

Given $$X=A2BC1/3D3Taking$$ logarithm of both sides, we havelog⁡$$X=2log$$⁡$$A+log$$⁡B−$$13log$$⁡C−$$3log$$⁡DPartially differentiating, we haveΔ$$xx=2$$Δ$$AA+$$ΔBB−$$13$$ΔCC−$$3$$ΔDDPercentage error in $$A=2$$Δ$$AA=2$$×$$2$$%$$=4$$%Percentage error in $$B=$$Δ$$BB=2$$%Percentage error in $$C=13$$Δ$$CC=13$$×$$4$$%                                                   $$=43$$%Percentage error in $$D=3$$Δ$$DD=3$$×$$5$$%$$=15$$%We find that the minimum percentage error is contributed by C. Hence the correct choice is (3).

In the measurement of a physical quantity $X = \frac{A^{2} B}{C^{1 / 3} D^{3}}$ . The percentage errors introduced in the measurements of the quantities A, B, C and D are 2%, 2%, 4% and 5% respectively. Then the minimum amount of percentage of error in the measurement of X is contributed by:

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In the measurement of a physical quantity X=A2BC1/3D3. The percentage errors introduced in the measurements of the quantities A, B, C and D are 2%, 2%, 4% and 5% respectively. Then the minimum amount of percentage of error in the measurement of X is contributed by:

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In the measurement of a physical quantity $X = \frac{A^{2} B}{C^{1 / 3} D^{3}}$ . The percentage errors introduced in the measurements of the quantities A, B, C and D are 2%, 2%, 4% and 5% respectively. Then the minimum amount of percentage of error in the measurement of X is contributed by: