A simple pendulum is oscillating with frequency ' F ' on the surface of the earth. It is taken to a depth R 3 below the surface of earth. ( R= radius of earth). The frequency of oscillation at depth R / 3 is

Step-by-step solution

The frequency of the pendulum at the surface is given as f = 1 2 g l At depth the formula for gravitational acceteration is g _ eff = g (1- d R ) For d= R 3 , g (1- 1 3 ) The frequency at depth d = R 3 f _ d = 1 2 g (1- 1 3 ) l = 1 2 2 ~g 3 l Take the ratio of both frequencies aligned f _ d f & = 2 3 f _ d & = F 1.5 ( f = F ) aligned