The length of a simple pendulum is increased by 44%. The percentage increase in its time period will be ( in percentage) ______ .Correct answer is '20'. Can you explain this answer?

Question

Answer

The length of a simple pendulum is increased by 44%. The percentage increase in its time period will be 20%.

Explanation:
When the length of a simple pendulum is increased, the time period of the pendulum also changes. The time period is defined as the time taken for one complete oscillation of the pendulum.

Formula:
The time period (T) of a simple pendulum is given by the formula:

T = 2π√(L/g)

Where:
T = Time period of the pendulum
L = Length of the pendulum
g = Acceleration due to gravity (approximately 9.8 m/s^2)

Step 1: Calculate the initial time period:
Let's assume the initial length of the pendulum is L1, and the initial time period is T1. Using the formula mentioned above, we can calculate T1.

T1 = 2π√(L1/g)

Step 2: Calculate the new length of the pendulum:
The length of the pendulum is increased by 44%. Let's calculate the new length of the pendulum, L2.

L2 = L1 + 0.44L1
= 1.44L1

Step 3: Calculate the new time period:
Using the formula mentioned above, we can calculate the new time period, T2.

T2 = 2π√(L2/g)
= 2π√((1.44L1)/g)
= 2π(1.2)√(L1/g)
= 1.2(2π√(L1/g))
= 1.2T1

Step 4: Calculate the percentage increase in time period:
To calculate the percentage increase, we can use the following formula:

Percentage Increase = ((T2 - T1) / T1) * 100

Substituting the values, we get:

Percentage Increase = ((1.2T1 - T1) / T1) * 100
= (0.2T1 / T1) * 100
= 20%

Therefore, the percentage increase in the time period of the simple pendulum when the length is increased by 44% is 20%.

Answer

For a simple pendulum

Let the increase in time period be t, then

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