A heavy ball is hung by a 5.0 m long string to construct a simple pendulum. It executes small oscillations. Determine the frequency if the setup is moved to the moon, where the acceleration due to lunar gravitation is

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Quantrex Academy · Accepted Answer

Correct answer: D. 1 2π 3 Hz

The frequency of a simple pendulum is given by the formula:

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

Given the length of the pendulum

L = 5.0 \text{ m}

and the acceleration due to gravity on the moon

g' = 1.67 \text{ m/s}^2

.

Approximating

1.67 \text{ m/s}^2

as

\dfrac{5}{3} \text{ m/s}^2

and substituting the values:

f = \dfrac{1}{2\pi} \sqrt{\dfrac{5/3}{5}}

f = \dfrac{1}{2\pi} \sqrt{\dfrac{1}{3}}

f = \dfrac{1}{2\pi \sqrt{3}} \text{ Hz}

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

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