Answer to Question #159265 in Physics for Pergold Cage

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 such a system called physical pendulum depends on its moment of inertia, which is 5/3 mr^2:

$$T=2\pi\sqrt{\frac{I}{mgh}}=2\pi\sqrt{\frac{5r^2}{3g(r+l)}},$$

where l - length of the thread. Therefore, the period is

$$T=\frac{0.31}{\sqrt{0.12+l}}\text{ s}.$$