A 2 kg mass is attached to a massless, 0.5 m string and is used as a simple pendulum by extendin

step 1 Hi, in the given problem, as we know, time period of a simple pendulum is given as t is equal to

A 2 kg mass is attached to a massless, 0.5 m string and is...

A 2 $\mathrm{kg}$ mass is attached to a massless, 0.5 $\mathrm{m}$ string and is used as a simple pendulum by extending it to an angle $\theta=5^{\circ}$ and allowing it to oscilate. Which of the following changes will change the period of the pendulum? Select two answers. (A) Replacing the mass with a 1 kg mass (B) Changing the initial extension of the pendulum to a $10^{\circ}$ angle (C) Replacing the string with a 0.25 $\mathrm{m}$ string (D) Moving the pendulum to the surface of the Moon

A 2 $\mathrm{kg}$ mass is attached to a massless, 0.5 $\mathrm{m}$ string and is used as a
simple pendulum by extending it to an angle $\theta=5^{\circ}$ and allowing it to oscilate. Which of the following changes will change the period of the pendulum? Select two answers.
(A) Replacing the mass with a 1 kg mass
(B) Changing the initial extension of the pendulum to a $10^{\circ}$ angle
(C) Replacing the string with a 0.25 $\mathrm{m}$ string
(D) Moving the pendulum to the surface of the Moon

Key Concepts

Gravitational Acceleration Dependence

The period of a simple pendulum is affected by the local gravitational acceleration. Moving the pendulum to a location with a different g value (such as from Earth to the Moon) will change the period, since the period is proportional to the inverse square root of the gravitational acceleration.

Pendulum Period Formula

The period of a simple pendulum, under the small-angle approximation, is given by the formula T = 2??(L/g), where L is the length of the pendulum and g is the local acceleration due to gravity. This formula shows that the period is influenced solely by the length of the pendulum and the gravitational field, not by the mass of the pendulum bob.

Mass Independence

In the study of pendulums, a critical concept is that the period of oscillation does not depend on the mass of the bob. This means that swapping out masses will have no effect on the period, which is a defining characteristic of ideal simple pendulums in uniform gravitational fields.

Small-Angle Approximation

The small-angle approximation facilitates the derivation of the simple pendulum's period formula by assuming that sin(?) is approximately equal to ? in radians for small angles. This approximation implies that slight changes in the initial displacement angle have negligible effects on the period, as long as the angle remains sufficiently small.

Transcript

Please give Ace some feedback