Question

The time period of a simple pendulum is directly related to the square root of its length. An 8-foot pendulum has a period of 3.2 seconds. Round all answers off to the nearest hundredth. Find the period for each of these:

a. A grandfather clock that has a pendulum of length 3 feet.

b. A mantle clock that has a pendulum of length 6 inches.

c. The longest pendulum in the world whose length was 4440 feet.

d. If you wanted to make a pendulum clock having a time period of 10 seconds, how long should the pendulum be?

e. A pendulum in Boston, Massachusetts has a time period of one quarter of a minute. How long is the pendulum? If the average story is 10 feet high, what is the minimum height, in stories, of a building that could contain this pendulum?

Answer 1

As we have time period of simple pendulum is direvtly related to square root of its length.

So if time period is T and length of pendulum is l .

So we can write it as:

Now we camn insert proportional constant.

For l = 8 foot , T = 3.2 sec

So

So

(a) Length of grandfather clock is 3 feet = 3 ft

So period of grandfather clock is:

(b) Length of mantle clock is = 6 inches

So length in foot (l) = 0.5 ft

So time period of mantle clock is:

(c) Longest pendulum in world have length is = 4440 feet

So time period is:

(d) Id pendulum clock have time period is 10 sec

Then length of pendulum is:

(e)

One quarter of minute is = 15 sec

So length of pendulum is: