A physical pendulum consists of a spherical bob of radius r and mass m suspended from a string (Figure). The distance from the center of the sphere to the point of support is L. When r is much less than L such a pendulum is often treated as a simple pendulum of length L.

(a) Show that the period for small oscillations is given by

the period of a simple pendulum of length L.

(b) Show that when r is much smaller than L, the period is approximately T ≈ T₀ (1 + r²/5L²).

(c) If L = 1 m and r = 2 cm, find the error when the approximation T = T₀ is used for this pendulum. How large must the radius of the bob be for the error to be 1%?

Transcribed Image Text:

2r2 where To 512 = To. = 27JL/g is T = T1+