Answer:
The height of the tower is 20.81 metres.
Explanation:
Extracting the key information from the question:-
*** The height of a tower needs to be determined.
*** A spool of thread is tied to a small rock to create the principle of simple pendulum.
*** The thread with the rock is hung down the centre of a staircase of the tower.
*** The period of the oscillation of the pendulum is 9.15 seconds.
*** Acceleration due to gravity will be taken as 9.8 metres per second.
*** We are simply required to calculate the height of the tower.
Now, since the period of the oscillation of the pendulum is 9.15 seconds, we will then first determine the angular frequency of the pendulum using the formula:-
w = 2π/T
Where, "w" is the angular frequency.
π will be taken as 3.14
T is the period of oscillation (9.15 seconds).
We will then solve for the angular frequency:
w = (2 × 3.14)/9.15
w = 6.28/9.15
w = 0.686 rad/sec
With the knowledge of the angular frequency of the pendulum, we can now calculate the height of the tower using the formula:
w = √(g/L)
Where, w = angular frequency
g = acceleration due to gravity
L = length (height of the tower).
Since "w" = 0.686 rad/sec and acceleration due to gravity is 9.8 metres per second, we can then determine/calculate the height of the tower by substituting appropriately and then making "L" the subject of the formula. That is:
√(g/L) = w
We then square both sides of the equation.
g/L = w^2
Cross multiply
L×(w^2) = g
L = g/(w^2)
We then substitute:
L = 9.8/(0.686^2)
L = 9.8/0.471
L = 20.81 metres
Therefore the height of the tower is 20.81 metres.
