A simple pendulum is suspended from the ceiling of a stationary elevator and it oscillates with a small amplitude if the elevator accelerates upwards, the

Options

A. frequency of oscillation of pendulum increases
B. frequency of the oscillations of the pendulum decreases
C. pendulum stops oscillating
D. time period of oscillations remain same but the amplitude increases

Answer

To solve the problem regarding the behavior of a simple pendulum in an upward accelerating elevator, we can follow these steps:

### Step 1: Understand the System
A simple pendulum consists of a mass (bob) attached to a string of length \( L \) that swings back and forth. The motion of the pendulum is influenced by gravitational force.

### Step 2: Identify the Effective Gravity
When the elevator accelerates upward with acceleration \( a \), the effective gravitational force acting on the pendulum changes. The effective acceleration due to gravity \( g_{\text{effective}} \) can be expressed as:
\[ g_{\text{effective}} = g + a \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

### Step 3: Write the Formula for Time Period
The time period \( T \) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
When the elevator accelerates upward, we replace \( g \) with \( g_{\text{effective}} \):
\[ T' = 2\pi \sqrt{\frac{L}{g + a}} \]

### Step 4: Analyze the Effect on Time Period
Since \( g + a > g \), it follows that:
\[ T' = 2\pi \sqrt{\frac{L}{g + a}} < T = 2\pi \sqrt{\frac{L}{g}} \]
This means that the time period \( T' \) decreases when the elevator accelerates upward.

### Step 5: Determine the Effect on Frequency
Frequency \( f \) is the reciprocal of the time period:
\[ f = \frac{1}{T} \]
Since the time period \( T' \) decreases, the frequency \( f' \) will increase:
\[ f' = \frac{1}{T'} > f = \frac{1}{T} \]

### Conclusion
Thus, when the elevator accelerates upwards, the frequency of oscillation of the pendulum increases.

### Final Answer
The correct option is **A: frequency of oscillation of pendulum increases**.

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