Question-05 A physical quantity A can be determined by measuring parameters B, C, D and E using the relation A=\frac{B^3 C^4}{D^7 E^8}. If the maximum errors in the measurement are b %, c %, d % and e % then maximum error in the value of A is
(A) (\alpha b + \beta c - \gamma d - \delta e)\%
(B) (b + c - d - e)\%
(C) (\alpha b + \beta c + \gamma d + \delta e)\%
(D) (b + c + d + e)\%
Answer : (C)
Explanation:
Given: A=\frac{B^\alpha C^\beta}{D^\gamma E^\delta}
Error contributed by B = \alpha\times\left(\frac{\Delta B}{B}\times100\right)
= \alpha\times b\%
Error contributed by C = \beta\times\left(\frac{\Delta C}{C}\times100\right)
= \beta\times c\%
Error contributed by D = \gamma\times\left(\frac{\Delta D}{D}\times100\right)
= \gamma\times d\%
Error contributed by E = \delta\times\left(\frac{\Delta E}{E}\times100\right)
= \delta\times e\%
∴ Percentage error in A is given as,
\frac{\Delta A}{A}\times100 = (% error contributed by B)
- (% error contributed by C)
- (% error contributed by D)
- (% error contributed by E)
= (\alpha b+\beta c+\gamma d+\delta e)\%