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)

Decreases

Answer 2

On going below depth $h$ from the surface of earth. The value of $g^{\prime}$ below is given by $g'=g\left(1-\frac{h}{R_{e}}\right)$ 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.