Level 1: A Child Stands Up on a Swing: Does the Period Change?
A swinging rod against a pendulum.
A uniform rod 1 m long swings about one end, and a simple pendulum 1 m long swings beside it, both through small angles. Which has the longer period, and by what factor?
For a body pivoted at one point, the period is T = 2π√(I/mgd), where d is the distance from the pivot to the centre of mass. For the rod, I = mL²/3 and d = L/2.
The rod behaves like a simple pendulum only two thirds as long, so the simple pendulum has the longer period, by √1.5 ≈ 1.22. The rod's mass is spread along it, and the parts near the pivot swing back quickly.
Every Level 2 starts from a quick question, Level 1, and changes one thing. Seeing what that change does is the skill JEE Main tests. Try it here, free and with no signup, then read the worked answer.
