A physical pendulum is composed of a disc whose center of gravity is attached to a thin rod.The disc has a moment of inertia of 1/2 MR².The mass of the disc is 500 gm and has a radius of 4.00 cm.The length of the rod is 50.0 cm.The period of the physical pendulum is A) 1.24 sec. B) 1.42 sec. C) 1.74 sec. D) 1.90 sec. E) 2.25 sec.

Question

Quizplus · Accepted Answer

The period of a physical pendulum is given by: T = 2π√(I/mgd), where I is the moment of inertia about the pivot point, m is the mass of the pendulum, g is the acceleration due to gravity, and d is the distance between the center of gravity and the pivot point.

In this case, we have: 
- I = ½MR² = ½(0.5 kg)(0.04 m)² = 1.6×10⁻³ kg m² (using the given moment of inertia formula and the values of mass and radius) 
- m = 0.5 kg (given) 
- g = 9.81 m/s² (standard value for acceleration due to gravity) 
- d = 0.5 m (given length of the rod)

Plugging in these values, we get: 
T = 2π√(1.6×10⁻³ kg m² / (0.5 kg × 9.81 m/s² × 0.5 m)) ≈ 1.42 sec

Therefore, the best choice is B: 1.42 sec.

A Physical Pendulum Is Composed of a Disc Whose Center