MATHEMATICS

JAMB 2004 - Question 15

Mathematics 2004 JAMB Past Questions - Question 15: The length L of a simple pendulum varies directly as the square of its period T.if a pendulum with period 4 sec is 64cm long.find the length of s pendulum whose period is 9 sec.

The length L of a simple pendulum varies directly as the square of its period T.if a pendulum with period 4 sec is 64cm long.find the length of s pendulum whose period is 9 sec.
A:
B:
C:
D:
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Correct Answer

D

Explanation

If the length L of a simple pendulum varies directly as the square of its period T, we can write the equation as L = kT², where k is the constant of proportionality.Given that a pendulum with a period of 4 seconds is 64 cm long, we can substitute these values into the equation to find the value of k:64 = k * 4²64 = k * 16Dividing both sides of the equation by 16, we get:k = 4Now that we have the value of k, we can use it to find the length of a pendulum whose period is 9 seconds:L = k * T²L = 4 * 9²L = 4 * 81L = 324Therefore, the length of the pendulum with a period of 9 seconds is 324 cm.