The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64 cm long, find the length of pendulum...

The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64 cm long, find the length of pendulum whose period is 9 sec

Answer Details

The problem describes a direct variation between the length of a simple pendulum and the square of its period, which means that we can write the relationship as: L = kT^2 where L is the length of the pendulum, T is its period, and k is a constant of proportionality. To find the value of k, we can use the information given in the problem that a pendulum with a period of 4 seconds has a length of 64 cm. Substituting these values into the equation above, we get: 64 = k(4^2) 64 = 16k k = 4 Now that we know the value of k, we can use the same equation to find the length of a pendulum with a period of 9 seconds: L = 4(9^2) L = 324 Therefore, the length of the pendulum whose period is 9 seconds is 324 cm.