Which of the following assumptions is made in a simple pendulum experiment? The: Select one: A. Initial angle of oscillation munt be large B. Bob has a finite size C. Bob has a definite mass D. Suspending string is in extensible
The correct answer and explanation is:
The correct answer is: D. Suspending string is inextensible.
In a simple pendulum experiment, several assumptions are made to simplify the analysis of its motion. The most important assumption is that the string or rod from which the pendulum bob is suspended is inextensible. This means that the length of the string does not change during the pendulum’s motion, ensuring that the pendulum’s oscillation depends only on the gravitational force and the length of the string.
The reason this assumption is critical is that if the string were extensible (able to stretch), the period of oscillation would change, and the system would behave differently. An extensible string would introduce additional forces, such as elastic restoring forces, which would complicate the analysis of the pendulum’s motion.
Another key assumption often made in a simple pendulum experiment is that the bob has a definite mass (option C). This allows the analysis to focus on the forces acting on the bob, such as gravity and tension, without considering the effects of mass distribution. However, the exact mass of the bob is not typically the primary concern in the idealized model of a simple pendulum.
Additionally, the bob should be treated as a point mass, meaning its size is considered negligible compared to the length of the string. Therefore, option B, “Bob has a finite size,” is not a correct assumption for a simple pendulum experiment. The assumption of a point mass simplifies the problem and focuses on the center of mass of the bob, where all the forces are assumed to act.
Finally, the initial angle of oscillation is typically assumed to be small (less than 15 degrees), as this ensures that the motion approximates simple harmonic motion. If the angle is too large, the approximation does not hold, and the system may behave in a more complex way. Thus, option A is not entirely true for a simple pendulum experiment, as the angle is assumed to be small for the linear approximation to be valid.