Question

If period of the pendulum in preceding sample problem were 24s how tall would the tower be ?

Answer 1

143 m.

Step-by-step explanation:

We have to use the equation for the period of a simple pendulum, and solve for length of pendulum.

`T=2\pi\sqrt{(l)/(g) }`

Here l length of pendulum which is equal to height of tower because it touches the almost the floor and g is acceleration due to gravity.

Given
`T=24s, g=9.8m/s^2`.

Substitute the given values, we get

`24s=2\pi\sqrt{(l)/(9.8m/s^2) }`

`((24s)/(2\pi))^2*9.8m/s^2 =l`

`l=143m`

Thus, the height of tower is 143 m.

Answer 2

So length of pendulum is 143.129 m

Step-by-step explanation:

We have given period of simple pendulum is 2 sec

We have to find the length of simple pendulum

Let the length of pendulum is l

Acceleration due to gravity
`g=9.8m/sec^2` is

Time period is given by
`T=2\pi \sqrt{(l)/(g)}`

So
`24=2* 3.14* \sqrt{(l)/(9.8)}`

`\sqrt{(l)/(9.8)}=3.821`

Squaring both side

`{(l)/(9.8)}=14.60`

l =143.129 m

So length of pendulum is 143.129 m