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A simple pendulum, consisting of a mass on a string of length L, is undergoing small oscillations with amplitude A.
1. The mass is increased by a factor of four. What is true about the period?
Choose the best answer.
a. The period is halved.
b. The period increases by a factor of four.
c. The period remains unchanged.
d. The period doubles.
e. The period decreases by a factor of four.

Respuesta :

Answer:

A. Period is halved

Explanation:

The period of a pendulum swing, T, is given in terms of mass as:

[tex]T = 2\pi \sqrt{\frac{I}{mgL} }[/tex]

where I = moment of inertia

m = mass of the pendulum

g = acceleration due to gravity

h = Length of string

If the mass is increased by a factor of 4, that means:

M = 4m

(M = new mass)

The new period of the pendulum, [tex]T_n[/tex], will now be:

[tex]T_n = 2\pi \sqrt{\frac{I}{MgL} }\\\\\\T_n = 2\pi \sqrt{\frac{I}{4mgL} }\\\\\\T_n = 2\pi \sqrt{\frac{1}{4} * \frac{I}{mgL} }\\\\\\T_n = \frac{2\pi}{2} \sqrt{\frac{I}{mgL} }\\\\\\T_n = \frac{1}{2} * 2\pi \sqrt{\frac{I}{mgL} }\\\\\\T_n = \frac{1}{2} * T[/tex]

Hence, the period is halved.

Answer:

C

Explanation:

Mass doesn't affect period

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