The time period of a pendulum of length 'l' and mass of the bob 'm' is T. Time period of a pendulum with mass of the bob 2m and length l is ______.

Options

A. T
B. 2T
C. 3T
D. 4T

Explanation

To find the time period of a pendulum with a bob mass of 2m and length l, we can follow these steps:

### 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:
- \( T \) is the time period,
- \( l \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity.

2. **Identify the Variables**:
In the original scenario, the pendulum has:
- Length \( l \)
- Mass of the bob \( m \)
The time period for this pendulum is given as \( T \).

3. **Consider the New Pendulum**:
The new pendulum has:
- Length \( l \) (same as the original)
- Mass of the bob \( 2m \) (double the original mass)

4. **Analyze the Effect of Mass on Time Period**:
According to the formula, the time period of a simple pendulum does not depend on the mass of the bob. It only depends on the length of the pendulum and the acceleration due to gravity.

5. **Conclusion**:
Since the length of the pendulum remains the same and the time period is independent of the mass of the bob, the time period for the new pendulum with mass \( 2m \) will still be:
\[ T = 2\pi \sqrt{\frac{l}{g}} \]
Therefore, the time period remains \( T \).

### Final Answer:
The time period of a pendulum with mass \( 2m \) and length \( l \) is \( T \).

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