Solve the problem. Round as appropriate.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 2.5 sec when the length is 25 inches, what is the period when L = 3.0625 inches?
A) 3.5 sec
B) 3.25 sec
C) 3 sec
D) 0.875 sec

Question

Quizplus · Accepted Answer

The period of vibration $P$ is directly proportional to the square root of the length $L$, so $P = k\sqrt{L}$, where $k$ is the constant of proportionality. Given $P = 2.5$ sec when $L = 25$ inches, we can find $k$ by substituting these values: $2.5 = k\sqrt{25}$, leading to $k = 0.5$. For $L = 3.0625$ inches, $P = 0.5\sqrt{3.0625} = 0.5 \times 1.75 = 0.875$ sec.

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