Question

two simple pendulums, a and b, are each 3.0 m long, and the period of pendulum a is t. pendulum a is twice as heavy as pendulum b. what is the period of pendulum b?
a) t/2
b) 2t
c) t√2
d) t/√2
e) t

Explanation:

Step1: Recall the formula for the period of a simple pendulum

The period \( T \) of a simple pendulum is given by the formula \( T = 2\pi\sqrt{\frac{l}{g}} \), where \( l \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

Step2: Analyze the given information

We are given that both pendulums A and B have the same length (\( l_A = l_B = 3.0 \, \text{m} \)) and they are in the same gravitational field (so \( g \) is the same for both). The mass of pendulum A is twice that of pendulum B, but from the formula, we can see that the period of a simple pendulum does not depend on the mass of the pendulum bob.

Step3: Determine the period of pendulum B

Since the length \( l \) and the gravitational acceleration \( g \) are the same for both pendulums A and B, their periods should be the same. Given that the period of pendulum A is \( T \), the period of pendulum B should also be \( T \).

Answer:

e) \( T \)