Question

a physical quantity X is calculated from the relation X is equals to A cube B square / root cd calculate percentage error xif a ,b ,c and d are measured respectively within error 1% 3% 4%and2%

Answer 1

Given,
X = A³ B²/√(CD)
Then, formula of % error is given by
% error in X = 3 × % error in A + 2 × % error in B + 1/2 × % error in C + 1/2 × % error in D

Here , % error in A = 1%
% error in B = 3%
% error in C = 4%
% error in D = 2 %

Now, % error in X = 3 × 1 % + 2 × 3% + 1/2 × 4% + 1/2 × 2 %
= 3% + 6% + 2% + 1%
= 12%

Answer 2

Given equation Is :

X= A³B²/√CD

Percentage error in A= 1%
Percentage error in B= 3%
Percentage error in C = 4%
Percentage error in D= 2%

To calculate : Percentage error in X

Formula to be used :

Percentage error in X:

ΔXx100/X= 3 xΔAx100/A  + 2x ΔBx100/B  + 1/2 ΔCx100/C  + 1/2 ΔDx100/D

On substituting the values of % errror in A,B ,C and D respectively we get,

Percentage error in X= 3%+2x3% + 2% +1% = 3%+6% +2%+1%=12%

∴Percentage error in X is 12 %