In an experiment, the percentage of error occurred in the measurement of physical quantities AAA, BBB, CCC and DDD are 1%1\%1%, 2%2\%2%, 3%3\%3% and 4%4\%4% respectively. Then the maximum percentage of X=A2B1/2C1/3D3X = \frac{A^2 B^{1/2}}{C^{1/3} D^3}X=C1/3D3A2B1/2
error in the measurement XXX will be
3/13 %
16%
– 10%
10%
x=A2B12C13D3x = \frac{A^2 B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^3}x=C31D3A2B21
% error, Δxx×100=2ΔAA×100+12ΔBB×100+13ΔCC×100+3ΔDD×100\% \text{ error, } \frac{\Delta x}{x} \times 100 = 2 \frac{\Delta A}{A} \times 100 + \frac{1}{2} \frac{\Delta B}{B} \times 100 + \frac{1}{3} \frac{\Delta C}{C} \times 100 + 3 \frac{\Delta D}{D} \times 100% error, xΔx×100=2AΔA×100+21BΔB×100+31CΔC×100+3DΔD×100
=2×1%+12×2%+13×3%+3×4%= 2 \times 1\% + \frac{1}{2} \times 2\% + \frac{1}{3} \times 3\% + 3 \times 4\%=2×1%+21×2%+31×3%+3×4%
=2%+1%+1%+12%= 2\% + 1\% + 1\% + 12\%=2%+1%+1%+12%
=16%= 16\%=16%
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