Question

The Young modulus (Y) of a material is given by Y=(WL)/(pir^(2)l). If the percentage error in W, L, r and l are 0.5%, 1%, 3%" and "4% respectively then maximum percentage error in Y is -

Answer 1

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Answer 2

Answer:

The maximum percentage error in Y is 11.5%.

Explanation:

As per the formula given in the question we have,

$Y=\frac{WL}{\pi r^2l}$         (1)

Where,

Y=youngs modulus

W=weight of the material

πr²=cross sectional area of the material

L=length of the material

l=change in the length of the material

So, the maximum percentage error in "Y" is given as,

$\frac{\Delta Y}{Y} =\frac{\Delta W}{W} +\frac{\Delta L}{L} +2\frac{\Delta r}{r} +\frac{\Delta l}{l}$        (2)

From the question we have,

%error in W($\frac{\Delta W}{W}$)=0.5%

%error in W($\frac{\Delta L}{L}$)=1%

%error in W($\frac{\Delta r}{r}$)=3%

%error in W($\frac{\Delta l}{l}$)=4%

By substituting the required values in equation (2) we get;

$\frac{\Delta Y}{Y} =0.5\% +1\% +2\times 3\%+4\%$

$\frac{\Delta Y}{Y} =0.5\% +1\% +6\%+4\%$

$\frac{\Delta Y}{Y} =11.5\%$

Hence, the maximum percentage error in Y is 11.5%.