A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. If follows that
(a) its velocity is constant
(b) its acceleration is constant
(c) its kinetic energy is constant
(d) it moves in a circular path.
(c) its kinetic energy is constant
(d) it moves in a circular path.
Explanation:
Since the force is always perpendicular to the velocity, it means there is no displacement in the direction of force i.e. no work is done on the particle. Hence no change in the Kinetic Energy, so K.E. is constant. Hence answer (c).
Since the particle is acted upon by a force, its velocity must change according to Newtons Second Law of Motion and this change must be in the direction of the force. Since the force is always perpendicular to the velocity it only changes its direction, not the magnitude. It results in movement of the particle in a circular path in which the force is always along the radius. Hence answer (d), not (a).
Again the acceleration is in the radial direction (i.e. in the direction of force) and in the circular motion, this direction of acceleration always changes because the direction of force changes constantly. So (b) is not correct.