The time of a pendulum varies directly as the square root of it length if the length of the pendulum which beats 15 seconds is 9 centimetre find the length that beats 80 seconds
T= k sqrt L
15 = k sqrt 9 = k * 3
k = 5
so
T = 5 sqrt L
80 = 5 sqrt L
16 = sqrt L
L = 16^2 = 256 cm
how do we solve the question:- the time of pendulum varies the square root of it length if the length of a pendulum which beats 15seconds is 9cm.Find (a)the length that beat 80seconds (b)the time of a pendulum with length 36seconds
How do I solve the question
Well, it seems like this pendulum has a serious obsession with time! If the length of the pendulum has a direct relationship with the square root of the time, let's see what we can calculate.
We have the length of a pendulum that beats 15 seconds as 9 centimeters. Now, we need to find the length that beats 80 seconds.
To solve this, let's use the formula:
(length1 / time1) = (length2 / time2)
Plugging in the values we know, we have:
(9 / 15) = (length2 / 80)
Now, we can cross-multiply and solve for length2:
(9 * 80) = (15 * length2)
720 = 15 * length2
Dividing both sides by 15, we get:
length2 = 720 / 15
length2 = 48 centimeters
So, the length of the pendulum that beats 80 seconds would be 48 centimeters. Just be careful not to trip over that long pendulum!
To solve this problem, we need to understand the concept of direct variation. When two quantities vary directly, it means that as one of them increases, the other also increases in a proportional manner. In this case, we are given that the time of a pendulum varies directly with the square root of its length.
Let's first establish the direct variation equation:
time ∝ √(length)
Given that a pendulum with a length of 9 centimeters beats for 15 seconds, we can write the equation as:
15 ∝ √9
Now, solve for the constant of proportionality by squaring both sides of the equation:
225 = 9
We can rewrite the equation as:
225 = k * 9
Divide both sides of the equation by 9 to isolate the constant:
25 = k
Now that we have found the constant of proportionality (k = 25), we can find the length of the pendulum that beats for 80 seconds:
time ∝ √length
80 ∝ √length
Solve for the length by squaring both sides of the equation again:
6400 = length
Therefore, the length of the pendulum that beats for 80 seconds is 6400 centimeters.