The bob of a simple pendulum of mass `100g` is oscillating with a time period of `1.42s`. If the bob is replaced by another bob of mass `150g` but of same radius, the new time period of oscillation

Options

A. `1.14s`
B. `1.32s`
C. `1.42s`
D. `1.6s`

Explanation

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the first bob, \( m_1 = 100 \, \text{g} = 0.1 \, \text{kg} \) (though mass does not affect the time period).
- Time period of the first bob, \( T_1 = 1.42 \, \text{s} \).
- Mass of the second bob, \( m_2 = 150 \, \text{g} = 0.15 \, \text{kg} \) (again, mass does not affect the time period).

2. **Understand the Formula:**
- The time period \( T \) depends only on the length \( L \) of the pendulum and the acceleration due to gravity \( g \). It does not depend on the mass of the bob.

3. **Determine the Length \( L \):**
- Since the problem states that the radius of the bob remains the same and the length of the pendulum \( L \) is unchanged, we can conclude that \( L \) remains constant.

4. **Calculate the New Time Period:**
- Since the time period is independent of the mass of the bob, the new time period \( T_2 \) will be the same as the original time period \( T_1 \):
\[ T_2 = T_1 = 1.42 \, \text{s} \]

5. **Conclusion:**
- The new time period of oscillation when the bob is replaced by another bob of mass \( 150 \, \text{g} \) is still \( 1.42 \, \text{s} \).

### Final Answer:
The new time period of oscillation is \( 1.42 \, \text{s} \).