How tall is the tower in the following case?You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor...

How tall is the tower in the following case?

You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 27 s. The acceleration of gravity is 9.81 m/s^2. How tall is the tower?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The time period T of a pendulum to complete one cycle while it swings is given by T = 2*pi*sqrt(L/g) where L is the length of the pendulum and g is the acceleration due to gravity.

In the question it is noticed that a pendulum extending from the ceiling almost touches the floor and that its period is 27 s. The acceleration of gravity is 9.81 m/s^2.

Substituting these values in the formula for time period

27 = 2*pi*sqrt(L/9.81)

=> L/9.81 = (27/2*pi)^2

=> L = (27/2*pi)^2*9.81 m

=> L = 181.14 m

The height of the tower is approximately equal to 181.14 m

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