Question

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

Answer 1

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

Explanation:

Let m is the mass of the object and v is its velocity. So, 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 %.

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Topic : Percentage error

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