Question

If the percentage error in the measurement of mass is 20percent and in velocity is 15 percent then percentage error in the momentum will be

Answer 1

Percentage error, $\dfrac{\Delta p}{p}=35\%$

Explanation:

It is given that,

The percentage error in the measurement of mass is 20 percent and in velocity is 15 percent.

$\dfrac{\Delta m}{m}=20\%$

$\dfrac{\Delta v}{v}=15\%$

The momentum of an object is given by :

$p=mv$

Taking log both sides,

$log\ p=log\ m+log\ v$

Now, Differentiating the both sides of the Equation,

$\dfrac{\Delta p}{p}=\dfrac{\Delta m}{m}+\dfrac{\Delta v}{v}$

$\dfrac{\Delta p}{p}=20+15$

$\dfrac{\Delta p}{p}=35\%$

So, the percentage error in the momentum will be 35%. Hence, this is the required solution.

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Topic : Percentage error

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