Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be

The correct option is 8%.

Step-by-step Derivation:

The formula for kinetic energy ($K$) of an object of mass $m$ moving with speed $v$ is given by:

$K=\frac{1}{2}m{v}^2$

When calculating errors, the constant coefficient ($\frac{1}{2}$) does not contribute to the error. Therefore, the relative error in the kinetic energy is the sum of the relative error in mass and twice the relative error in speed (since speed is raised to the power of 2):

$\frac{\Delta K}{K}=\frac{\Delta m}{m}+2\left(\frac{\Delta v}{v}\right)$

To find the maximum percentage error, we multiply both sides of the equation by 100:

$\left(\frac{\Delta K}{K}\times 100\right)=\left(\frac{\Delta m}{m}\times 100\right)+2\left(\frac{\Delta v}{v}\times 100\right)$

We are given the following values in the problem:
1. Percentage error in mass, $\frac{\Delta m}{m}\times 100=2\%$
2. Percentage error in speed, $\frac{\Delta v}{v}\times 100=3\%$

Substituting these values into our percentage error formula:

$\text{Percentage error in }K=2\%+2\times 3\%$

$\text{Percentage error in }K=2\%+6\%=8\%$

Thus, the error in the estimate of kinetic energy is 8%.