Question: The period T in seconds and the length L in inches of the pendulum are related as T = 2πL384. Find the length of the pendulum in inches with period of 6 seconds.

A ) 350.17
B ) 102.76
C ) 580.64
D ) 298.32

Steps to derive

1 T = 2πL384

2 T² = (2π)2L384
 [Square on both sides.]

3 384 · T² = (2π)2L
 [Multiply both sides with 384.]

4 L = T2⋅384(2π)2
 [Divide both sides by (2π )².]

5 L = (6)2⋅384(2π)2
 [Substitute 6 for T.]

6 L = 350.17 inches.

7 The length of the pendulum = 350.17 inches.



Hence the right answer is Option A

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