If there is a positive error of 50% in the measurement of velocity of a body, then the error in the measurement of kinetic energy is

The correct option is 100%.

Step-by-Step Explanation:

The kinetic energy ($K$) of a body of mass $m$ moving with a velocity $v$ is given by the formula:
$K=\frac{1}{2}m{v}^2$

Assuming the measurement of mass ($m$) is constant and has no error, the relationship between the relative error in kinetic energy and the relative error in velocity can be found using the error approximation method (differentiation):
$\frac{\Delta K}{K}=2·\frac{\Delta v}{v}$

To find the percentage error, we multiply both sides of the equation by 100:
$\left(\frac{\Delta K}{K}·100\right)=2·\left(\frac{\Delta v}{v}·100\right)$

We are given that the percentage error in the measurement of velocity is 50%:
$\frac{\Delta v}{v}·100=50\%$

Substituting this value into our error formula:
$\text{Percentage error in kinetic energy}=2·50\%=100\%$

Thus, by using the standard linear error relation, the error in the measurement of kinetic energy is determined to be 100%.