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If P= c^3b^2/cd andpercentage error in c,b,d are1% 2% and 3% respectively , calculate the % error in P |
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Answer» tion:Answer:The percentage error in P is 13%.Explanation:GIVEN that,P=a^3b^2(\sqrt{c}d)P=a 3 b 2 ( c d)a = 1%b= 3%c=4%d=2%The percentage error in P\dfrac{\DELTA P}{P}\times100=[3\times\dfrac{\Delta a}{a}+2\times\dfrac{\Delta b}{b}+\dfrac{1}{2}\dfrac{\Delta C}{C}+\dfrac{\Delta d}{d}]\times100 PΔP ×100=[3× aΔa +2× bΔb + 21 CΔC + dΔd ]×100\dfrac{\Delta P}{P}\times100=[3\times\dfrac{1}{100}+2\times\dfrac{3}{100}+\dfrac{1}{2}\times\dfrac{4}{100}+\dfrac{2}{100}]\toimes100 PΔP ×100=[3× 1001 +2× 1003 + 21 × 1004 + 1002 ]\toimes100\dfrac{\Delta P}{P}\times100=[\dfrac{3+6+2+2}{100}]\times100 PΔP ×100=[ 1003+6+2+2 ]×100\dfrac{\Delta P}{P}\times100=[\dfrac{13}{100}]\times100 PΔP ×100=[ 10013 ]×100\dfrac{\Delta P}{P}\times100=13\% PΔP ×100=13%Hence, The percentage error in P is 13%. |
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