If the percentage errors in the measurement of mass and velocity of a body are $2\%$ and $3\%$ respe

Question

If the percentage errors in the measurement of mass and velocity of a body are $2\%$ and $3\%$ respectively, what is the maximum percentage error in the estimation of its kinetic energy?

Professor PC Thomas Classes · Answer

Kinetic energy $K = \frac{1}{2}mv^2$. The percentage error is given by $\frac{\Delta K}{K} 	imes 100 = (\frac{\Delta m}{m} 	imes 100) + 2(\frac{\Delta v}{v} 	imes 100) = 2\% + 2(3\%) = 2\% + 6\% = 8\%$.