In an experiment to measure the centripetal force acting on a...

The formula for centripetal force is given by

$F = \dfrac{mv^2}{r}$

The maximum percentage error in the calculation of force is

$\dfrac{\Delta F}{F} \times 100 = \left( \dfrac{\Delta m}{m} + 2\dfrac{\Delta v}{v} + \dfrac{\Delta r}{r} \right) \times 100$

First, calculate the individual percentage errors:
Percentage error in mass = $\dfrac{0.5}{50} \times 100 = 1\%$
Percentage error in velocity = $\dfrac{0.4}{20} \times 100 = 2\%$
Percentage error in radius = $\dfrac{0.3}{10} \times 100 = 3\%$

Substitute these values into the error equation:

$\dfrac{\Delta F}{F} \times 100 = 1\% + 2(2\%) + 3\%$
$\dfrac{\Delta F}{F} \times 100 = 1\% + 4\% + 3\% = 8\%$

Answer: $8\%$