Velocity vector and acceleration vector in a uniform circular motion are related as

Options

A. both in the same direction
B. perpendicular to each other
C. both in opposite direction
D. not related to each other

Explanation

To solve the question regarding the relationship between the velocity vector and acceleration vector in uniform circular motion, we can follow these steps:

### Step 1: Understand the Concept of Uniform Circular Motion
In uniform circular motion, an object moves along a circular path with a constant speed. Although the speed remains constant, the direction of the velocity vector changes continuously.

**Hint:** Recall that uniform circular motion involves constant speed but changing direction.

### Step 2: Identify the Velocity Vector
At any point on the circular path, the velocity vector is tangent to the circle. This means that the direction of the velocity vector is always along the tangent line at that point.

**Hint:** Visualize or sketch the circular path and draw tangent lines at various points to see the direction of the velocity vector.

### Step 3: Identify the Acceleration Vector
In uniform circular motion, the acceleration vector is directed towards the center of the circle. This is known as centripetal acceleration, which is responsible for changing the direction of the velocity vector.

**Hint:** Remember that acceleration in circular motion always points towards the center of the circular path.

### Step 4: Analyze the Relationship Between Velocity and Acceleration
Since the velocity vector is tangent to the circle and the acceleration vector is directed towards the center, these two vectors are perpendicular to each other at every point along the circular path.

**Hint:** Use the concept of right angles to confirm that a tangent line and a radius (pointing towards the center) form a right angle.

### Step 5: Conclusion
Thus, in uniform circular motion, the velocity vector and the acceleration vector are always perpendicular to each other.

**Final Answer:** The correct relationship is that the velocity vector and acceleration vector in uniform circular motion are perpendicular to each other.