Question

A particle moves with uniform speed along a circular path. The direction of its acceleration (if any) is-

• A. Radially outward
• B. Radially inward
• C. Tangentially
• D. No acceleration

Hint:

In circular motion:

• Velocity is always tangential to the path.

• Centripetal acceleration is always directed toward the center.

• If speed is constant, only the direction of velocity changes.
Hence, uniform circular motion is an accelerated motion.

Answer 1

The Correct Option is B

Concept: Acceleration is defined as the rate of change of velocity with time. Velocity is a vector quantity, meaning that both its magnitude and direction are important. In uniform circular motion, although the speed remains constant, the direction of motion changes continuously. Therefore, the velocity changes continuously and an acceleration must be present.

Step 1: Understand the motion of the particle.
Consider a particle moving along a circular path with constant speed. At every point on the circle, the direction of velocity is along the tangent to the path. As the particle moves from one point to another, the direction of this tangent changes continuously. Hence, the velocity vector changes even though its magnitude remains constant.

Step 2: Determine whether acceleration exists.
Since acceleration depends on the change in velocity and not merely on the change in speed, \[ \text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}} \] the continuous change in the direction of velocity produces acceleration. Therefore, a particle moving in a circle with uniform speed definitely possesses acceleration.

Step 3: Identify the direction of acceleration.
The acceleration responsible for keeping the particle on the circular path is called

centripetal acceleration. This acceleration always acts toward the center of the circle. Its magnitude is given by :contentReference[oaicite:0]index=0 where

• \(v\) = speed of the particle

• \(r\) = radius of the circular path
Because it always points toward the center, its direction is radially inward.

Step 4: Select the correct option.
Therefore, the direction of acceleration in uniform circular motion is \[ \boxed{\text{Radially inward}} \]