An aeroplane is flying with a uniform speed of 100 km/h along the circumference of a circle. The change in velocity in half the revolution will be in km/h)

Options

A. 100
B. 150
C. 200
D. 300

Explanation

To solve the problem of finding the change in velocity of an aeroplane flying with a uniform speed of 100 km/h along the circumference of a circle after half a revolution, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Velocity**:
- Velocity is a vector quantity, which means it has both magnitude and direction. The magnitude is the speed, and the direction is the path in which the object is moving.

2. **Identify the Initial and Final Positions**:
- Let's denote the starting point of the aeroplane as point A and the point after half a revolution as point B.

3. **Determine the Initial Velocity (VA)**:
- At point A, the aeroplane is flying upwards with a speed of 100 km/h. Therefore, the initial velocity can be represented as:
\[ V_A = +100 \text{ km/h} \quad (\text{upward direction is considered positive}) \]

4. **Determine the Final Velocity (VB)**:
- After half a revolution, the aeroplane reaches point B, where it is flying downwards with the same speed of 100 km/h. Thus, the final velocity can be represented as:
\[ V_B = -100 \text{ km/h} \quad (\text{downward direction is considered negative}) \]

5. **Calculate the Change in Velocity (ΔV)**:
- The change in velocity is given by the formula:
\[ \Delta V = V_B - V_A \]
- Substituting the values we found:
\[ \Delta V = (-100 \text{ km/h}) - (+100 \text{ km/h}) = -100 \text{ km/h} - 100 \text{ km/h} = -200 \text{ km/h} \]

6. **Interpret the Result**:
- The negative sign indicates that the direction of the velocity has changed from upward to downward. The magnitude of the change in velocity is 200 km/h.

### Final Answer:
The change in velocity after half a revolution is **200 km/h**.

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