The percentage errors in the measurement of mass and momentum of an object are 1% and 2% respectively. The percentage error in the measurement of kinetic energy of the object will be:

To find the percentage error in kinetic energy, we first identify the physical relationship between kinetic energy ($K$), momentum ($p$), and mass ($m$). Kinetic energy is defined by the formula $K = \frac{p^2}{2m}$ .

According to the rules for combining errors, if a quantity depends on multiple observations raised to certain powers, the maximum relative error is the sum of the relative errors of each observation multiplied by their respective exponents . Applying this to our formula:

$\frac{\Delta K}{K} = 2\left(\frac{\Delta p}{p}\right) + 1\left(\frac{\Delta m}{m}\right)$

1. Identify given errors: Percentage error in mass ($\frac{\Delta m}{m} \times 100$) = 1%; Percentage error in momentum ($\frac{\Delta p}{p} \times 100$) = 2%.
2. Calculate percentage error in $K$: $\% \text{ error in } K = 2(2\%) + 1(1\%) = 4\% + 1\% = 5\%.$

Thus, the percentage error in the measurement of kinetic energy is 5%.