If the mass of a pendulum is doubled, the time period

Options

A. becomes double
B. becomes half
C. becomes 4 times
D. remains the same

Explanation

To determine how the time period of a pendulum is affected when the mass of the pendulum is doubled, 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:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( T \) is the time period,
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity.

### Step 2: Identify the variables in the formula.
From the formula, we can see that the time period \( T \) depends on:
- The length \( L \) of the pendulum,
- The acceleration due to gravity \( g \).

### Step 3: Analyze the effect of changing the mass of the pendulum.
The mass of the pendulum (or the bob) does not appear in the formula for the time period. This indicates that the time period is independent of the mass of the bob.

### Step 4: Conclude the effect of doubling the mass.
Since the time period \( T \) does not depend on the mass of the bob, if we double the mass of the pendulum, the time period remains unchanged.

### Final Answer:
Thus, if the mass of the pendulum is doubled, the time period remains the same.

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