The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 2 sec when the length is 16 inches, what is the period when L = 6.25 inches?
(Round to the nearest hundredth.)
A)2.50 sec
B)1.25 sec
C)2.75 sec
D)2.25 sec

Question

Quizplus · Accepted Answer

The relationship between the period of vibration (P) and the length (L) of a pendulum is given by $P = k\sqrt{L}$, where $k$ is a constant. Given $P = 2$ sec when $L = 16$ inches, we can find $k$ by substituting these values: $2 = k\sqrt{16}$ or $2 = 4k$, so $k = 0.5$. For $L = 6.25$ inches, $P = 0.5\sqrt{6.25} = 0.5 \times 2.5 = 1.25$ sec.

The Period of Vibration P for a Pendulum Varies Directly