In a laboratory experiment, the centripetal force acting on a body moving in a circular path is to be determined. The mass of the body is measured as (50.0 ± 0.5) g , its speed as (4.00 ± 0.06) m/s , and the radius of

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Correct answer: B. 4.5\%

The centripetal force is given by the formula

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

.

The maximum percentage error in the measurement of force is given by:

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

Given values are:

m = 50.0 \text{ g}

,

\Delta m = 0.5 \text{ g}

v = 4.00 \text{ m/s}

,

\Delta v = 0.06 \text{ m/s}

r = 80.0 \text{ cm}

,

\Delta r = 0.4 \text{ cm}

Substituting the values:

\dfrac{\Delta F}{F} \times 100 = \left( \dfrac{0.5}{50.0} + 2 \times \dfrac{0.06}{4.00} + \dfrac{0.4}{80.0} \right) \times 100

\dfrac{\Delta F}{F} \times 100 = (0.01 + 2 \times 0.015 + 0.005) \times 100

\dfrac{\Delta F}{F} \times 100 = (0.01 + 0.03 + 0.005) \times 100

\dfrac{\Delta F}{F} \times 100 = 0.045 \times 100 = 4.5\%

Answer:

4.5\%

In a laboratory experiment, the centripetal force acting on a body...

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