The time period in seconds, T, for a pendulum to swing is directly proportional to the square root of its length in metres. A pendulum of length 25cm takes a period of 1 second. What length will take a period of 1.2 seconds?
T = k√L so T/√L is constant.
You want L such that
1.2/√L = 1/√25
Why did the pendulum go to the doctor? Because it needed a check-up!
To solve this problem, we can use the formula for the period of a pendulum: T = k√L, where T is the period, L is the length of the pendulum, and k is a constant of proportionality.
We're given that a pendulum of length 25 cm (which is equivalent to 0.25 m) takes a period of 1 second. Let's plug those values into the formula:
1 = k√0.25
Now, let's solve for k:
k = 1 / √0.25
k = 1 / 0.5
k = 2
Now that we have the value of k, we can find the length of the pendulum that takes a period of 1.2 seconds:
1.2 = 2√L
Divide both sides by 2:
0.6 = √L
Square both sides:
0.36 = L
So, a pendulum with a length of 0.36 meters (or 36 cm) will take a period of 1.2 seconds. Just make sure you don't get tangled up in its humor!
To find the length of the pendulum that will take a period of 1.2 seconds, we can set up a proportion using the given information.
Let L be the length of the pendulum in meters, and let T be the period in seconds.
According to the given information, we have the following:
L = 0.25 meters (since the length is given as 25 cm)
T = 1 second
Using the given information, we can determine the constant of proportionality by rearranging the equation:
T = k * sqrt(L)
1 = k * sqrt(0.25)
Simplifying the equation:
1 = k * 0.5
k = 1 / 0.5
k = 2
Now, we can use the constant of proportionality to find the length of the pendulum that will take a period of 1.2 seconds:
T = 1.2 seconds (new period)
1.2 = 2 * sqrt(L)
Dividing both sides by 2:
0.6 = sqrt(L)
Squaring both sides to eliminate the square root:
0.6^2 = L
0.36 = L
Therefore, a pendulum of length 0.36 meters (or 36 cm) will take a period of 1.2 seconds.
To solve this problem, we need to use the formula provided that relates the time period and the length of the pendulum. The formula states:
T = k * sqrt(L)
Where T is the time period in seconds, L is the length of the pendulum in meters, and k is a constant of proportionality.
We are given that a pendulum with a length of 25 cm (or 0.25 meters) has a time period of 1 second. Using this information, we can substitute the values into the formula to find the value of k:
1 = k * sqrt(0.25)
Let's solve this equation for k:
sqrt(0.25) = 0.5
So, we have:
1 = k * 0.5
Dividing both sides of the equation by 0.5:
1 / 0.5 = k
k = 2
Now that we have the value of k, we can use it to find the length, L, that will result in a time period of 1.2 seconds.
T = 1.2 seconds
Using the formula:
1.2 = 2 * sqrt(L)
Dividing both sides by 2:
0.6 = sqrt(L)
Squaring both sides to eliminate the square root:
0.6^2 = L
L = 0.36 meters
Therefore, a pendulum with a length of 0.36 meters will have a time period of 1.2 seconds.