A simple pendulum, suspended from the ceiling of a stationary van, has time period T . If the van starts moving with a uniform velocity the period of the pendulum will be

Options

A. Less than T
B. Equal to 2 T
C. Greater than T
D. Unchanged

Answer

To solve the problem regarding the time period of a simple pendulum suspended from the ceiling of a stationary van when the van starts moving with a uniform velocity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- Initially, the pendulum is at rest in a stationary van. The time period \( T \) of the 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. **Analyzing the Motion of the Van**:
- When the van starts moving with a uniform velocity, it is important to note that uniform velocity means there is no acceleration acting on the van. Therefore, the forces acting on the pendulum remain unchanged.

3. **Forces Acting on the Pendulum**:
- The forces acting on the pendulum are:
- The gravitational force \( mg \) acting downward.
- The tension \( T \) in the string acting upward.
- Since the van is moving uniformly, the pendulum does not experience any additional forces in the horizontal direction.

4. **Effect on the Time Period**:
- The time period of a simple pendulum depends only on the length of the pendulum and the acceleration due to gravity. Since neither \( L \) nor \( g \) changes when the van moves with uniform velocity, the time period remains the same.

5. **Conclusion**:
- Therefore, the time period of the pendulum when the van is moving with uniform velocity is still:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- Thus, the period of the pendulum will remain unchanged.

### Final Answer:
The time period of the pendulum will be unchanged, i.e., it remains \( T \).

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