The centripetal force acting on a particle moving in a circular path is calculated by measuring its mass, speed, and the radius of the path. If the percentage errors in the measurement of mass, speed, and radius are 1\%

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Correct answer: D. 6.0\%

The formula for centripetal force is given by:

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

The maximum percentage error in the measurement of force is:

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

Given the percentage errors:

\dfrac{\Delta m}{m} \times 100 = 1\%

\dfrac{\Delta v}{v} \times 100 = 1.5\%

\dfrac{\Delta r}{r} \times 100 = 2\%

Substituting these values into the error equation:

\dfrac{\Delta F}{F} \times 100 = 1\% + 2(1.5\%) + 2\%

\dfrac{\Delta F}{F} \times 100 = 1\% + 3\% + 2\% = 6.0\%

Answer:

6.0\%

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