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

Options

A. 0.44
B. 0.22
C. 0.2
D. 0.11

Explanation

To solve the problem of finding the percentage increase in the time period of a simple pendulum when its length is increased by 44%, we can follow these steps:

### Step 1: Understand the formula for the time period of a simple pendulum
The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

### Step 2: Define the initial length and time period
Let the initial length of the pendulum be \( L \). Therefore, the initial time period \( T \) can be expressed as:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]

### Step 3: Calculate the new length after the increase
If the length of the pendulum is increased by 44%, the new length \( L' \) can be calculated as:
\[ L' = L + 0.44L = 1.44L \]

### Step 4: Calculate the new time period with the new length
Now, we can find the new time period \( T' \) using the new length \( L' \):
\[ T' = 2\pi \sqrt{\frac{L'}{g}} = 2\pi \sqrt{\frac{1.44L}{g}} = 2\pi \sqrt{1.44} \sqrt{\frac{L}{g}} = 1.2 \cdot 2\pi \sqrt{\frac{L}{g}} = 1.2T \]

### Step 5: Calculate the percentage increase in the time period
The percentage increase in the time period can be calculated using the formula:
\[ \text{Percentage Increase} = \frac{T' - T}{T} \times 100\% \]
Substituting \( T' = 1.2T \):
\[ \text{Percentage Increase} = \frac{1.2T - T}{T} \times 100\% = \frac{0.2T}{T} \times 100\% = 20\% \]

### Conclusion
The percentage increase in the time period of the pendulum when its length is increased by 44% is **20%**.

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