A heavy ball is hung by a 5.0 m long string to construct a simple...

A heavy ball is hung by a

5.0 \text{ m}

long string to construct a simple pendulum. It executes small oscillations. How many oscillations does it complete per second? (Assume standard acceleration due to gravity on Earth,

g = 9.8 \text{ m/s}^2

Options

A $\dfrac{0.35}{\pi} \text{ Hz}$
B $\dfrac{\pi}{0.70} \text{ Hz}$
C $\dfrac{1.4}{\pi} \text{ Hz}$
D $\dfrac{0.70}{\pi} \text{ Hz}$

Correct answer

D. $\dfrac{0.70}{\pi} \text{ Hz}$

Step-by-step solution

The frequency of a simple pendulum is given by the formula

f = \dfrac{1}{2\pi} \sqrt{\dfrac{g}{L}}

.

Substituting the given values

L = 5.0 \text{ m}

and

g = 9.8 \text{ m/s}^2

f = \dfrac{1}{2\pi} \sqrt{\dfrac{9.8}{5.0}}

f = \dfrac{1}{2\pi} \sqrt{1.96}

f = \dfrac{1.4}{2\pi}

f = \dfrac{0.70}{\pi} \text{ Hz}

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