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Units And Measurement

Question
CBSEENPH11020601

In an experiment, four quantities a,b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows:

P = fraction numerator straight a cubed straight b squared over denominator cd end fraction space percent sign, error in P is

  • 14 %

  • 10 %

  • 7 %

  • 4 %

Solution

A.

14 %

Here, P = fraction numerator straight a cubed straight b squared over denominator cd end fraction
Therefore,
fraction numerator increment straight P over denominator straight P end fraction space x space 100
open parentheses fraction numerator 3 increment straight a over denominator straight a end fraction plus fraction numerator 2 increment b over denominator b end fraction plus fraction numerator increment c over denominator c end fraction plus fraction numerator increment d over denominator d end fraction close parentheses x 100
3 fraction numerator increment straight a over denominator straight a end fraction straight x 100 space plus space 2 space fraction numerator increment straight b over denominator straight b end fraction straight x 100 space plus space fraction numerator increment straight c over denominator straight c end fraction straight x 100 space plus space fraction numerator increment straight d over denominator straight d end fraction straight x 100
= 3 x1 + 2 x 2 + 3 +4 
= 3 + 4 + 3 + 4
= 14 %