In a seconds pendulum, mass of bob is 30 gm . If it is replaced by 90 gm mass. Then its time period will

Options

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

Answer

To solve the problem, we need to analyze the behavior of a seconds pendulum and how its time period is affected by the mass of the bob.

### Step-by-Step Solution:

1. **Understanding the Seconds Pendulum**:
A seconds pendulum is defined as a pendulum that takes exactly one second to complete one half of its oscillation (from the mean position to one extreme) and two seconds for a full oscillation (back to the mean position). Thus, the time period (T) of a seconds pendulum is 2 seconds.

2. **Formula for Time Period of a Pendulum**:
The time period 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.

3. **Mass of the Bob**:
In this problem, we are given that the mass of the bob is initially 30 gm and is replaced by a 90 gm mass. It’s important to note that in the formula for the time period, mass does not appear. This indicates that the time period of a pendulum does not depend on the mass of the bob.

4. **Effect of Changing the Mass**:
Since the time period of a simple pendulum is independent of the mass of the bob, changing the mass from 30 gm to 90 gm will not affect the time period as long as the length of the pendulum remains constant.

5. **Conclusion**:
Therefore, the time period of the pendulum after replacing the bob with a 90 gm mass will still be:
\[ T = 2 \text{ seconds} \]

### Final Answer:
The time period will remain **2 seconds**.