In a second’s pendulum, mass of Bob is 50 g. If it is replaced by 100 g mass, then its period will be.

Options

A. 1 s
B. 2 s
C. 3 s
D. 4 s

Answer

To solve the problem, we need to determine how the period of a pendulum is affected when the mass of the bob is changed.

### Step-by-Step Solution:

1. **Understanding the Pendulum**: A second's pendulum is defined as a pendulum that has a period of 2 seconds. This means it takes 1 second to swing in one direction and 1 second to return.

2. **Given Information**:
- The mass of the bob is initially 50 g and is replaced by a 100 g mass.
- The length of the pendulum (L) is 1 meter (as a second's pendulum has a specific length).

3. **Formula for the Period of a Pendulum**:
The formula for the period (T) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( T \) = period of the pendulum
- \( L \) = length of the pendulum
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, m/s^2 \))

4. **Analyzing the Change in Mass**:
- The formula for the period of a pendulum does not include the mass of the bob. This means that changing the mass of the bob does not affect the period of the pendulum.
- Since the length of the pendulum (L) and the acceleration due to gravity (g) remain constant, the period will also remain constant.

5. **Conclusion**:
- Therefore, even after replacing the 50 g mass with a 100 g mass, the period of the pendulum remains the same.
- The period of the pendulum is still \( T = 2 \) seconds.

### Final Answer:
The period of the pendulum after replacing the mass will still be **2 seconds**.

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