Answer :
Final answer:
To find the period of oscillation for the system, consider it as a physical pendulum and use the period formula T = 2π √(I / mgd) after computing the moment of inertia I and the distance d from the pivot to the center of mass.
Explanation:
To determine the period of oscillation for the given system, we first need to consider the system as a physical pendulum. A physical pendulum consists of an extended body that rotates about a pivot point. In this case, the rod with the attached weight can be considered as such, and we will use the formula for the period T of a physical pendulum:
T = 2π √(I / mgd)
where:
- I is the moment of inertia of the rod and the attached weight about the pivot point,
- m is the mass of the rod,
- g is the acceleration due to gravity (≈ 9.81 m/s²),
- d is the distance from the pivot point to the center of mass of the system.
The moment of inertia I for a rod of length L pivoted at one end is ML²/3, and since the additional mass is very close to the other end, we can simply add its moment of inertia, which is md², where d is the distance of the mass from the pivot. So, we get:
I = ML²/3 + md².
However, because the mass of the rod is distributed, the center of mass is not simply at the midpoint. With the added mass at 195 cm, the center of mass shifts slightly towards the mass. This needs to be calculated as well.
Once the moment of inertia and center of mass have been calculated, the period T can be determined using the formula mentioned above.
