question_answer

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

A)  Increases

B)  Decreases

C)  First increases then decreases

D)  No effect

Correct Answer: B

Solution :

Ongoing below depth \[h\] from the surface of earth. The value of \[g\] below is given by\[g=g\left( 1-\frac{h}{{{R}_{e}}} \right)\]hence \[g\] decreases Also, Time period\[(T)=\frac{1}{frequency(n)}\] and        \[T=2\pi \sqrt{\frac{l}{g}}\] 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.