Answer to Question #158572 in Physics for Jocelyn Obena

Question

A Christmas ball in a shape of a hollow sphere is hung from the tree by a piece of thread attached to the surface of the ball. The mass and radius of the ball are 0.105kg and 0.12m, respectively. What will be its period of oscillation when slightly displaced from its equilibrium position? (Hint: I =5 3 𝑚𝑟 2 )

Answer 1

The period of small oscillations of an object with mass and volume that cannot be ignored depends on the moment of inertia:

$$T=2\pi\sqrt{\frac{I}{mgh}}.$$

The moment of inertia of such a system is (as given in the condition)

$$I=\frac53mr^2.$$

Assuming the hinge of the ball is at its surface, i.e., h = r, we have

$$T=2\pi\sqrt{\frac{5r}{3g}}=0.9\text{ s}.$$