A seconds pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket

Options

A. comes down with uniform accceleration
B. moves round the earth in a geostationaly orbit
C. moves up with a uniform veloctiy
D. moves up with uniform acceleration

Answer

To determine in which scenario the period of oscillation of a seconds pendulum decreases when mounted in a rocket, we need to analyze the relationship between the period of the pendulum and the effective gravitational acceleration acting on it.

### Step-by-Step Solution:

1. **Understanding the Pendulum's Period**:
The period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

2. **Identifying Effective Gravity in a Rocket**:
When the rocket accelerates, the effective gravitational acceleration \( g' \) acting on the pendulum changes. If the rocket accelerates upwards with an acceleration \( a \), the effective gravitational acceleration becomes:
\[ g' = g + a \]
Here, \( g \) is the acceleration due to gravity on Earth.

3. **Effect of Upward Acceleration**:
If the rocket is moving upwards with an acceleration \( a \), the effective gravitational acceleration \( g' \) increases. As \( g' \) increases, the period \( T \) of the pendulum can be expressed as:
\[ T' = 2\pi \sqrt{\frac{L}{g + a}} \]
Since \( g + a > g \), it follows that \( T' < T \). Therefore, the period of the pendulum decreases.

4. **Conclusion**:
The period of oscillation of the seconds pendulum decreases when the rocket moves upwards with uniform acceleration.

### Final Answer:
The period of oscillation decreases when the rocket is moving upwards with uniform acceleration.

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