A Christmas ornament made from a thin hollow glass sphere hangs from a small hook at its surface.It is observed to oscillate with a frequency of 2.50 Hz in a city where g = 9.80 m/s².What is the radius of the ornament? The moment of inertia of a hollow sphere of mass M and radius R about a point on its edge is 5MR²/3.

Question

Quizplus · Accepted Answer

We can use the formula for the frequency of oscillation of a simple pendulum:

f = 1/2π √(g/L)

where g is the acceleration due to gravity and L is the length of the pendulum. In this case, the glass sphere is acting as a simple pendulum, and its length L is equal to the radius of the sphere, r.

Rearranging the formula, we get:

r = g/4π^2 f^2

Plugging in the given values, we get:

r = 9.80 m/s^2 / (4π^2 x 2.50 Hz)^2
r = 2.38 cm

Finally, we can check that our answer is reasonable by comparing it to the dimensions of typical Christmas ornaments. A radius of around 2.38 cm seems reasonable for a small glass ornament. Therefore, the best choice is (C).

A Christmas Ornament Made from a Thin Hollow Glass Sphere