Question

if the effective length of a pendulum is infinite find time period?

Answer 1

if the effective length of a pendulum is infinite time period = 84.6 minutes

Answer 2

Take any instant t let position at t=P join the mean position of the pendulums bob to the centre of the earth join P to the centre of the Earth Let angle between both lines be Q at P: mg acts vertically downwards mgsinQ provides restoring force F= -mgsinQ a=F/m= -gsinQ.........(1) for Q<10 degrees sinQ=Q(in radians) = tanQ let distance between the mean position and P be x tan Q=x/R where R is radius of earth a= -gx/R but a= -w^2 X x therefore w=underroot of g/R time period= 2pi/w therefore T= 2pi underroot (g/R) that is 86 Minutes