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 28 s. the acceleration of gravity is 9.81 m/s 2 . how tall is the tower?

The height of the tower, where, the pendulum extending from the ceiling almost touches its floor is 195 meters.

Pendulum is the body which is pivoted a point and perform back and forth motion around that point by swinging due to the influence of gravity.

The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.

It can be given as,

Here, (g) is the gravitational force of Earth and (L) is the length of the pendulum.

The period of the pendulum is 28 s and the acceleration of gravity is 9.81 m/s². Thus the length of the pendulum is,

As, the pendulum extending from the ceiling almost touches the floor. Thus, the height of the tower, is equal to the length of the pendulum.

Thus, the height of the tower, where, the pendulum extending from the ceiling almost touches its floor is 195 meters.

Learn more about the time period of pendulum here;

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the approx height of the tower must be 195 m

Explanation:

As we know that time period of simple pendulum is given as

now we know that

now we have

now rearrange the terms to find the value of L

so the approx height of the tower must be 195 m

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.