Round your answer to two decimal places.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 3.5 sec when the length is 49 inches, what is the period when L = 5.0625
Inches?
A) 1.125 sec
B) 4 sec
C) 3.75 sec
D) 4.5 sec

Question

Quizplus · Accepted Answer

The period of vibration $P$ is directly proportional to the square root of the length $L$, so we can write $P = k\sqrt{L}$, where $k$ is the constant of proportionality. Given $P = 3.5$ sec when $L = 49$ inches, we can find $k$ by substituting these values: $3.5 = k\sqrt{49}$, which simplifies to $3.5 = k \times 7$, giving $k = 0.5$. For $L = 5.0625$ inches, $P = 0.5\sqrt{5.0625} = 0.5 \times 2.25 = 1.125$ sec.

Round Your Answer to Two Decimal Places