Question

A rod suspended at its end acts as a physical pendulum and swings with a period of 1. 4 s. What is the length of this physical pendulum? Assume that g=9.8 m/s2

Answer 1

The length of the physical pendulum is 0.98 meters.

Step-by-step explanation:

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

In this case, the period is given as 1.4s and g is given as 9.8 m/s². We can rearrange the equation to solve for the length of the pendulum: L = T²g/(4π²). Plugging in the values, we get L = (1.4)² * 9.8 / (4π²) = 0.98m.

Therefore, the length of the physical pendulum is 0.98 meters.

Answer 2

The length of the physical pendulum is approximately 0.099 m.

Step-by-step explanation:

A physical pendulum is a rigid body that is allowed to rotate about an axis of rotation. The period of a physical pendulum is given by the formula T = 2π√(I/mgd), where T is the period, I is the moment of inertia, m is the mass, g is the acceleration due to gravity, and d is the distance from the axis of rotation to the center of mass.

In this case, the period is given as 1.4 s and the acceleration due to gravity is 9.8 m/s². The length of the physical pendulum can be calculated by rearranging the formula as follows:

d = (T/(2π√g))^2 * (m/I)

Since the rod is suspended at its end, we can assume that the entire length of the rod is the distance from the axis of rotation to the center of mass. Therefore, the length of the physical pendulum is equal to the length of the rod.

Substituting the given values into the equation:

d = (1.4/(2π√9.8))^2 * (m/I)

d ≈ 0.099 m