Assertion: Time period of a simple pendulum having a hollow...

Assertion: Time period of a simple pendulum having a hollow sphere, filled with water, as bob then its time period increases continuously as water drains out. Reason: Effective length of above mentioned pendulum changes until all the water drains out. (A) $\mathrm{A}$ (B) B (C) $\mathrm{C}$ (D) D

Key Concepts

Simple Pendulum Dynamics

A simple pendulum is a mass suspended from a fixed point so that it can swing freely. The oscillation period of a simple pendulum is determined primarily by the length of the pendulum and the acceleration due to gravity, as given by the formula T = 2??(L/g). This model assumes that the mass acts as a point mass, meaning its internal distribution does not affect the period. However, if the mass distribution changes, as in a pendulum bob whose contents shift, the assumptions of the simple pendulum model are no longer strictly valid.

Effective Length

Effective length refers to the distance between the point of suspension and the center of mass of the pendulum bob. In any pendulum system, this effective length is crucial because it directly influences the time period of oscillation according to the formula T = 2??(L_eff/g). Changes in the mass distribution of the pendulum bob, such as when water drains from a hollow sphere, will shift the center of mass and consequently alter the effective length over time.

Center of Mass Variation

The center of mass of an object is the point where its mass is considered to be concentrated. In the scenario of a pendulum with a water-filled hollow sphere, as water drains out, the remaining mass redistributes within the sphere. This shift changes the position of the center of mass relative to the point of suspension, leading to a variation in the effective length of the pendulum. Since the time period of a pendulum depends on this effective length, this dynamic change results in a continuously changing period as the water drains.

Transcript

Please give Ace some feedback