The momentum ( p ) and mass ( m ) of a moving body are measured in...

The kinetic energy $K$ of a body is related to its momentum $p$ and mass $m$ by the formula:
$K = \dfrac{p^2}{2m}$

The maximum fractional error in kinetic energy is given by:
$\dfrac{\Delta K}{K} = 2\dfrac{\Delta p}{p} + \dfrac{\Delta m}{m}$

Multiplying by 100 to get the percentage error:
$\dfrac{\Delta K}{K} \times 100 = 2 \left( \dfrac{\Delta p}{p} \times 100 \right) + \left( \dfrac{\Delta m}{m} \times 100 \right)$

Given values:
$\dfrac{\Delta p}{p} \times 100 = \dfrac{1}{50} \times 100 = 2\%$
$\dfrac{\Delta m}{m} \times 100 = \dfrac{0.5}{10} \times 100 = 5\%$

Substituting these values into the error formula:
Percentage error in $K = 2(2\%) + 5\% = 4\% + 5\% = 9\%$

Answer: $9\%$