- #1

LCSphysicist

- 646

- 161

- Homework Statement
- A pendulum is constructed as a light thin-walled sphere of

radius R filled up with water and suspended at the point 0 from a

light rigid rod (Fig. 4.1.1). The distance between the point 0 and the

centre of the sphere is equal to 1. How many times will the small

oscillations of such a pendulum change after the water freezes? The

viscosity of water and the change of its volume on freezing are to

be neglected

- Relevant Equations
- All below

That's a good question, i am not sure how the water in liquid state will influence in the motion, but i imagine that can not exert any torque, i would say in the first case:

Hollow sphere inertia moment: 2mr²/3 + ml²

(2mr²/3 + ml²)θ'' = -mglθ (1)

In the second case, otherwise, we will have

2(m+m')r²/5 + (m+m')l² = -(m+m')glθ

Anyway, i am certain that have some error in (1), something say to me that the water can indeed exert a torque although it doesn't contribute to inertia moment, but, as i don't know the mechanics of a fluid, i am not sure.