A cabin is falling freely under gravity, what is the time period of a pendulum attached to its celling?

Options

A. zero
B. `oo`
C. 1 s
D. 2 s

Explanation

To solve the problem of finding the time period of a pendulum attached to the ceiling of a cabin that is falling freely under gravity, we can follow these steps:

### Step 1: Understand the scenario
The cabin is falling freely under the influence of gravity. This means that both the cabin and the pendulum inside it are accelerating downwards at the same rate, which is equal to the acceleration due to gravity (g).

### Step 2: Recall the formula for the time period of a pendulum
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 3: Determine the effective gravity in a freely falling frame
In a freely falling frame (like the cabin), the effective acceleration due to gravity (g') experienced by the pendulum is zero. This is because everything inside the cabin is in free fall, and there is no relative acceleration acting on the pendulum.

### Step 4: Substitute the effective gravity into the formula
Since the effective gravity \( g' = 0 \), we substitute this into the time period formula:
\[ T = 2\pi \sqrt{\frac{L}{0}} \]

### Step 5: Analyze the result
The expression \( \sqrt{\frac{L}{0}} \) leads to an undefined situation, which implies that the time period becomes infinite. This means that the pendulum does not oscillate at all in the freely falling cabin.

### Conclusion
Thus, the time period of the pendulum attached to the ceiling of the cabin that is falling freely under gravity is infinite.

### Final Answer
The time period of the pendulum is \( T = \infty \).

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