Question

Time period of is simple pendulum of length `L` is `T_(1)` and the point time peirod of a uniform rod of the same length `L` pivotal about one end and oscillating in vertical plane is `T_(2)`. Amplitude of oscillation in both the cased is small. The `T_(1)//T_(2)` is:

Answer 1

`T_(1)=2pisqrt((L)/(g))and T_(2)=2pisqrt((I)/(C))`
hwere `I=` moment of inertia of the rod about an axis through th pivot `=(1)/(3)mL^(2)` and `C=` restoring torque per unit angular displacement `=mgL//2`
`:. T_(2)=2pisqrt(((1//3)mL^(2))/(mgL//2))=2pisqrt((2L)/(3g))`
`:. (T_(1))/(T_(2))=sqrt((3)/(2))`