Physics

The length of a strip measured with a meter rod is 10.0 cm its width measured with a vernier caliper is 1.00 cm. The least count of the meter rod is 0.1 cm and that of vernier caliper caliper 0.01 cm water will be error in its area?


ANSWER

$$ \pm 2$$% 


SOLUTION

Given,

Least count of tape is $$0.1\,cm$$

Least count of Vernier caliper is $$0.01\,cm$$

Length, $$L=10\,cm$$

Width, $$W=1\,cm$$

$$area$$,$$A=Length\times width=L\times W$$

Take ln and differentiate,

$$ \dfrac{\Delta A}{A}=\dfrac{\Delta L}{L}+\dfrac{\Delta W}{W} $$

$$ \dfrac{\Delta A}{A}=\dfrac{0.1}{10}+\dfrac{0.01}{1}=0.02=2\,percent\, $$

Hence, error in area is $$\pm2$$ % 

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