Time period of a simple pendulum in a freely falling lift will be

Options

A. Finite
B. Inifinite
C. Zero
D. All of these

Answer

To find the time period of a simple pendulum in a freely falling lift, we can follow these steps:

### Step 1: Understand the formula for the time period of a simple pendulum
The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g_{\text{effective}}}} \]
where \( L \) is the length of the pendulum and \( g_{\text{effective}} \) is the effective acceleration due to gravity.

### Step 2: Analyze the situation in a freely falling lift
In a freely falling lift, the lift is accelerating downwards with an acceleration equal to \( g \) (the acceleration due to gravity). Therefore, the effective gravitational force acting on the pendulum becomes zero.

### Step 3: Determine the effective gravity
In the freely falling lift:
- The weight of the pendulum \( mg \) acts downwards.
- A pseudo force \( ma \) acts upwards, where \( a = g \) (the acceleration of the lift).

Since both forces are equal in magnitude but opposite in direction, the net force acting on the pendulum is:
\[ F_{\text{net}} = mg - mg = 0 \]
This means that the effective gravitational acceleration \( g_{\text{effective}} \) is zero.

### Step 4: Substitute \( g_{\text{effective}} \) into the time period formula
Now substituting \( g_{\text{effective}} = 0 \) into the time period formula:
\[ T = 2\pi \sqrt{\frac{L}{0}} \]
Since division by zero is undefined, we conclude that the time period \( T \) approaches infinity.

### Step 5: Conclusion
Thus, the time period of a simple pendulum in a freely falling lift is infinite.

### Final Answer
The time period of a simple pendulum in a freely falling lift will be infinite.

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