Question

A heavy brass ball is used to make a pendulum with a period of 5.5 seconds. how long is the cable that connects the pendulum ball to the ceiling?

(a) 4.7 m
(b) 6.2 m
(c) 7.5 m
(d) 8.7 m

Answer 1

Using the formula for the period of a simple pendulum, the length of the cable connecting the pendulum ball to the ceiling for a period of 5.5 seconds is calculated to be approximately 7.5 meters.

Step-by-step explanation:

The period T of a simple pendulum is determined by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth's surface).

To find the length L when the period T is given, we need to rearrange the formula to solve for L: L = (T/(2π))² * g. Substituting the given period T of 5.5 seconds and g as 9.81 m/s², we can calculate the length of the pendulum's cable.

Let’s calculate:

L = ((5.5 seconds / (2 * 3.14159))² * 9.81 m/s²)

L ≈ 7.5 meters

Therefore, the length of the cable connecting the pendulum ball to the ceiling is approximately 7.5 meters, which corresponds to answer choice (c).