Question

The percentage error in the measurement of mass and speed are $2\%$ and $3\%$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed

• A. $11\%$
• B. $8\%$
• C. $5\%$
• D. $1\%$

Answer 1

The correct option is B $8\%$

We know that,
Kinetic energy $K=\frac{1}{2}m{v}^2$
Fractional error in estimating Kinetic energy can be written as
$\frac{\Delta K}{K}=\frac{\Delta m}{m}+2\frac{\Delta v}{v}$
From this , Percentage error in estimating kinetic energy can be written as,
$\frac{\Delta K}{K}\times 100=(\frac{\Delta m}{m}\times 100)+2(\frac{\Delta v}{v}\times 100))$
In words, we can say that,
Percentage error in estimating Kinetic energy = Percentage error in measuring mass + $2\times$ Percentage error in measuring speed.
$\therefore$ From the data given in the question,
Maximum error in estimating Kinetic energy $=2+2\left(3\right)=8\%$

Thus, option (b) is the correct answer.