Read each statement below carefully and state, with reasons, if it is true or false :
(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.
(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.

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Solution

(a) False, the acceleration is towards the centre only in uniform circular motion. In non Uniform motion, acceleration has tangential component as well.
(b) True, the velocity is always tangential, if the motion is uniform or not.

(c) True, When particle returns to its original position after completing one cycle, its displacement is zero. Hence, average velocity and acceleration over one complete cycle is zero, which is null vector.

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Read each statement below carefully and state with reasons, if it is true or false:

(a) The magnitude of a vector is always a scalar, (b) each component of a vector is always a scalar, (c) the total path length is always equal to the magnitude of the displacement vector of a particle. (d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector.

Read each statement below carefully and state with reasons, if it is true or false :

(a) The magnitude of a vector is always a scalar,

(b) Each component of a vector is always a scalar,

(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time,

(e) Three vectors not lying in a plane can never add up to give a null vector.

The average acceleration vector for a particle having a uniform circular motion is

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