Question

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 = `(A^2B^(1/2))/(C^(1/3)D^3)`, will be:

Options

• – 10%

• 10%

• `(3/13)`%

• 16%

Answer 1

16%

Explanation:

Given: X = `(A^2B^(1/2))/(C^(1/3)D^3)`

Error contributed by A = `2 xx ((ΔA)/A xx 100)` = 2 × 1% = 2%

Error contributed by B = `1/2 xx ((ΔB)/B xx 100) = 1/2` × 2% = 1%

Error contributed by C = `1/3 xx ((ΔC)/C xx 100) = 1/3` × 3% = 1%

Error contributed by D = `3 xx ((ΔD)/D xx 100)` = 3 × 4 = 12%

∴ Percentage error in x is given as, `(Δx)/x xx 100` = (error contributed by A) + (error contributed by B) + (error contributed by C) + (error contributed by D)

= 2% + 1% + 1% + 12%

= 16%