question_answer

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

Correct Answer: B

Solution :

Key Idea: Value of acceleration due to gravity decreases on going below the surface of the earth. On going 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. Time period \[\text{(T) = }\frac{\text{1}}{\text{frequency(n)}}\] And                   \[T=2\pi \sqrt{\frac{l}{g}}\] where I 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.