Physics

The length, breadth and thickness of a block are measured with the help of a meter scale. given   $$ \ell $$ =(5.12 + 0.01)cm, b =(10.15 +0.01)cm, t=(5.28+0.01)cm. The percentage error in volume is:


ANSWER

0.48%


SOLUTION

Given that,

Length of the block $$l = (5.12+0.01) $$cm

Breadth of the block $$b = (10.15+0.01)$$ cm

Thickness of the block $$ t = (5.28+0.01)$$ cm

We know that,

Relative error in volume of cuboid

  $$ \dfrac{dV}{V}=\dfrac{dl}{l}+\dfrac{db}{b}+\dfrac{dt}{t} $$

 $$ \dfrac{dV}{V}=\dfrac{0.01}{5.12}+\dfrac{0.01}{10.15}+\dfrac{0.01}{5.28} $$

 $$ \dfrac{dV}{V}=\dfrac{1}{512}+\dfrac{1}{1015}+\dfrac{1}{528} $$


Now, the percentage error in volume

  $$ \dfrac{\Delta V}{V}\times 100=0.48 $$

 $$ \%\Delta V=0.48\% $$

Hence, the percentage error in volume is 0.48.

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