A uniform rod of mass m and length l is suspended through a light wire of length l and torsional constant k as shown in figure. Find the time perid iof the system makes a. small oscillations in the vertical plane about the suspension point and b. angular oscillations in the horizontal plane about the centre of the rod.

Options

A. `2pi sqrt((13l)/(12g)), 2pi sqrt((ml^(2))/(12K))`
B. `2pi sqrt((l)/(g)), 2pi sqrt((ml^(2))/(3K))`
C. `2pi sqrt((13l)/(12g)), 2pi sqrt((ml^(2))/(3K))`
D. `2pi sqrt((l)/(g)), 2pi sqrt((ml^(2))/(12K))`

Answer

A

Explanation

`T_(1) = 2pi sqrt((I)/(mgl)), I = (ml^(2))/(12) +ml^(2), T_(2) = 2pi sqrt((I)/(K)), I = (ml^(2))/(12)`