A torsion pendulum is a very useful tool for testing the equivalence principle (Sec. 25.2), for seeking evidence for hypothetical fifth (not to mention sixth!) forces, and for searching for deviations from gravity’s inverse-square law on submillimeter scales, which could arise from gravity being influenced by macroscopic higher spatial dimensions. It would be advantageous to design a torsion pendulum with a 1-day period (Fig. 11.17).Here we estimate whether this is possible. The pendulum consists of a thin cylindrical wire of length ℓ  and radius a. At the bottom of the wire are suspended three masses at the corners of an equilateral triangle at a distance b from the wire.

(a) Show that the longitudinal strain is

(b) What component of shear is responsible for the restoring force in the wire, which causes the torsion pendulum to oscillate?

(c) Show that the pendulum undergoes torsional oscillations with period

(d) Do you think you could design a pendulum that attains the goal of a 1-day period?

Figure 11.17

3mg (11.88a)