The periodic time of a simple pendulum of length 1 m and amplitude 2 cm is 5 seconds. If the amplitude is made 4 cm , its periodic time in seconds will be

Options

A. `4 sqrt(2) s`
B. 8s
C. 2s
D. 4s

Answer

To solve the problem, we need to determine how the periodic time of a simple pendulum changes when the amplitude is altered.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- The length of the pendulum (L) = 1 m
- Initial amplitude (A1) = 2 cm
- Initial periodic time (T1) = 5 seconds
- New amplitude (A2) = 4 cm

2. **Formula for the Period of a Simple Pendulum**:
The formula for the period (T) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity.

3. **Analyzing the Effect of Amplitude**:
- For small amplitudes, the period of a simple pendulum is independent of the amplitude. This means that as long as the amplitude is small (which both 2 cm and 4 cm are), the period remains constant.
- The periodic time is determined only by the length of the pendulum and the acceleration due to gravity.

4. **Conclusion**:
Since the length of the pendulum and the acceleration due to gravity remain unchanged, the new periodic time (T2) when the amplitude is increased to 4 cm will still be:
\[ T2 = T1 = 5 \text{ seconds} \]

### Final Answer:
The periodic time when the amplitude is made 4 cm will still be 5 seconds.

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