Question

A particle is moving in a circular path with a constant speed. What is the direction of its acceleration ?

• A. Tangential to the path
• B. Radially outward from the center
• C. Radially inward toward the center
• D. It has no acceleration

Hint:

Circular motion → acceleration always toward center (centripetal).

Answer 1

The Correct Option is C

Concept: In uniform circular motion, even though speed is constant, velocity changes direction continuously, resulting in acceleration called centripetal acceleration.

Step 1: Nature of velocity.
Velocity is a vector quantity. In circular motion:
• Magnitude (speed) remains constant
• Direction keeps changing Thus, acceleration must exist.

Step 2: Direction of acceleration.
The acceleration is always directed towards the center of the circle and is called centripetal acceleration.

Step 3: Mathematical expression.
\[ a = \frac{v^2}{r} \] where $v$ is speed and $r$ is radius.

Step 4: Evaluating options.

• Tangential → incorrect (only if speed changes)

• Outward → incorrect (centrifugal is pseudo force)

• Inward → correct

• No acceleration → incorrect

Step 5: Final evaluation.
Acceleration is directed radially inward. Final Conclusion:
Hence, the correct answer is option (3).