The time period of oscillations of a simple pendulum is 1 minute. If its length is increased b 44% then its new time period of oscillation will be

Options

A. 96s
B. 58s
C. 82s
D. 72s

Answer

To solve the problem, we need to find the new time period of a simple pendulum when its length is increased by 44%.

### Step-by-Step Solution:

1. **Understand the Formula for Time Period**:
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.

2. **Initial Time Period**:
According to the problem, the initial time period \( T \) is 1 minute, which is equal to 60 seconds.

3. **Calculate the New Length**:
The length of the pendulum is increased by 44%. If the original length is \( L \), the new length \( L' \) can be calculated as:
\[ L' = L + 0.44L = 1.44L \]

4. **Calculate the New Time Period**:
Now, we can find the new time period \( T' \) using the new length \( L' \):
\[ T' = 2\pi \sqrt{\frac{L'}{g}} = 2\pi \sqrt{\frac{1.44L}{g}} \]
This can be simplified as:
\[ T' = 2\pi \sqrt{1.44} \sqrt{\frac{L}{g}} = 2\pi \cdot 1.2 \sqrt{\frac{L}{g}} = 1.2 \cdot T \]

5. **Substitute the Initial Time Period**:
Since the initial time period \( T \) is 60 seconds:
\[ T' = 1.2 \cdot 60 = 72 \text{ seconds} \]

### Final Answer:
The new time period of oscillation after increasing the length by 44% is **72 seconds**.

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