Question

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 = a3 b2 / cd %.Error in P is what ??
please explain the solution.

Answer 1

quantity P is calculated as follows $P=\frac{a^3b^2}{cd}$

formula of % error should be,

% error in P = 3 × % error in a + 2 × % error in b + % error in c + % error in d

Given,

• % error in a = 1 %
• % error in b = 2 %
• % error in c = 3%
• % error in d = 4%

hence, % error in P = 3 × 1 + 2 × 2 + 3 + 4

= 3% + 4% + 3% + 4%

= 14%

hence, percentage error in P = 14%

Answer 2

Answer:

The percentage error in P is 14%.

Explanation:

Given that,

Percentage error of a = 1%

Percentage error of b = 2%

Percentage error of c = 3%

Percentage error of d = 4%

$P=\dfrac{a^3\ b^2}{cd}$

We know that,

Percentage error = $(\dfrac{\Delta x}{x}\times100)$

Therefore,

$(\dfrac{\Delta P}{P}\times100)=3(\dfrac{\Delta a}{a}\times100)+2x(\dfrac{\Delta b}{b}\times100)+1(\dfrac{\Delta c}{c}\times100)+1(\dfrac{\Delta d}{d}\times100)$

$(\dfrac{\Delta P}{P}\times100)=(3\times1+2\times2+1\times3+1\times4)$

$(\dfrac{\Delta P}{P}\times100)=14$

Hence, The percentage error in P is 14%.