Question

In uniform circular motion, the centripetal acceleration is

• A. towards the centre of the circular path and perpendicular to the instantaneous velocity
• B. a constant acceleration
• C. away from the centre of the circular path and perpendicular to the instantaneous velocity
• D. a variable acceleration making $45^\circ$ with the instantaneous velocity
• E. a variable acceleration, parallel to the instantaneous velocity

Hint:

Centripetal acceleration is always perpendicular to velocity and directed inward.

Answer 1

The Correct Option is A

Concept: Nature of centripetal acceleration in circular motion
In uniform circular motion:
• Speed is constant
• Direction of velocity continuously changes Acceleration is required to change direction → this is centripetal acceleration. ---

Step 1: Direction of centripetal acceleration

• Always directed towards the centre of the circle
• Responsible for keeping the particle in circular path ---

Step 2: Relation with velocity

• Velocity is tangential
• Acceleration is radial (towards centre) Thus: \[ \text{Angle between } \vec{v} \text{ and } \vec{a} = 90^\circ \] ---

Step 3: Check options

• (A) Correct: towards centre and perpendicular to velocity
• (B) Incorrect: magnitude constant but direction changes → acceleration is not constant vector
• (C) Incorrect: direction is not outward
• (D) Incorrect: not $45^\circ$
• (E) Incorrect: not parallel --- Final Answer: \[ \boxed{\text{(A)}} \]