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

Options

A. 96s
B. 20%
C. 82s
D. 72s

Answer

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 will 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 \( L_0 \). Therefore, the initial time period \( T_0 \) can be expressed as:
\[ T_0 = 2\pi \sqrt{\frac{L_0}{g}} \]

### Step 3: Calculate the new length after the increase.
The length of the pendulum is increased by 44%. Thus, the new length \( L \) can be calculated as:
\[ L = L_0 + 0.44L_0 = 1.44L_0 \]

### Step 4: Calculate the new time period.
Using the new length \( L \) in the time period formula, we get the new time period \( T \):
\[ T = 2\pi \sqrt{\frac{L}{g}} = 2\pi \sqrt{\frac{1.44L_0}{g}} = 2\pi \sqrt{1.44} \sqrt{\frac{L_0}{g}} = 2\pi \cdot 1.2 \sqrt{\frac{L_0}{g}} = 1.2 T_0 \]

### Step 5: Determine the percentage increase in the time period.
The percentage increase in the time period can be calculated using the formula:
\[ \text{Percentage Increase} = \frac{T - T_0}{T_0} \times 100\% \]
Substituting the values we have:
\[ \text{Percentage Increase} = \frac{1.2 T_0 - T_0}{T_0} \times 100\% = \frac{0.2 T_0}{T_0} \times 100\% = 20\% \]

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

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