Question

What effect occurs on the frequency of a pendulum if it is taken from the earth's surface to deep into a mine?

• A. Increases
• B. Decreases
• C. First increases then decreases
• D. No effect

Answer 1

Answer: (B)

On going below depth $h$ from the surface of earth. The value of $g^{\prime }$ below is given by $g^{\prime }=g\left(1-\frac{h}{R_e}\right)$ hence $g$ decreases
Also,
Time period $(T)=\frac{1}{\text{ frequency }(n)}$

and $T=2\pi \sqrt{\frac{1}{g}}$
where $l$ is length of pendulum.
$\therefore \frac{1}{n}=2\pi \sqrt{\frac{l}{g\left(1-\frac{h}{R_e}\right)}}$
Since, $n\propto g$, and $g$ decreases therefore frequency also decreases.