Read each statement below carefully and state, with reasons, if it is true or false:
The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre
False: In circular motion, if the speed is changing (non-uniform circular motion), there exists a tangential acceleration in addition to the centripetal acceleration. The net acceleration is the vector sum of both, and hence is not always directed along the radius towards the centre.
The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point
True: The velocity vector of a particle always represents the instantaneous direction of motion. By definition, this direction is always along the tangent to the path of the particle at that point.
The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector
True: In uniform circular motion, the acceleration (centripetal acceleration) is always directed towards the centre. Over one complete cycle, the acceleration vector points in all directions symmetrically. Due to this symmetry, the vector sum of acceleration over one complete cycle cancels out, resulting in a null vector.
Explanation
This question tests understanding of circular motion concepts from the Motion in a Plane chapter. Statement (a) is false because students often confuse uniform and non-uniform circular motion - only in uniform circular motion is acceleration purely centripetal. Statement (b) is a fundamental property of velocity. Statement (c) requires understanding that vector quantities have direction, and averaging over a complete cycle involves vector addition, not scalar averaging.