The length of a simple pendulum executing simple harmonic motion is increased by 21 % . The percentage increase in the time period of the pendulum of i
Question
The length of a simple pendulum executing simple harmonic motion is increased by 21 % . The percentage increase in the time period of the pendulum of i
Solution
To find the percentage increase in the time period of the pendulum, we can use the formula:
Percentage increase = (New time period - Old time period) / Old time period * 100
Let's assume the old time period of the pendulum is T.
Since the length of the pendulum is increased by 21%, the new length of the pendulum is 1.21 times the old length.
According to the formula for the time period of a simple pendulum, T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
So, the new time period of the pendulum can be calculated as follows:
New time period = 2π√(1.21L/g) = 2π√(1.21)√(L/g) = 1.1√(L/g) = 1.1T
Now, we can substitute the values into the percentage increase formula:
Percentage increase = (1.1T - T) / T * 100 = 0.1T / T * 100 = 10%
Therefore, the percentage increase in the time period of the pendulum is 10%.
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