A) particle going on the circle
B) Particle going along a straight line
C) Momentum of the particle constant
D) Acceleration of the particle constant
Correct Answer: B
Solution :
Let us discuss each option one by one: To keep a body moving on a circle, a force called centripetal force is continuously required to act on the body. To keep the momentum of a body constant, both magnitude and direction of its velocity should be forced to remain same. Thus a force is necessarily required to keep the momentum of a body constant when there is a tendency of either the magnitude of velocity or the direction to change. If we take the case of a particle moving in a circular path, a centripetal force must be acting on it. If it is desired that the momentum of this particle be kept constant, a force equal and opposite to the centripetal force must be applied on the particle. If we consider a body moving on a straight line path without friction, no force is required to keep the body moving with constant momentum but if friction is taken into account, a force must necessarily applied to maintain the momentum of the body constant. Thus there is only one situation when no force is required to maintain the momentum of a moving particle constant. This situation is the case of a body moving in a straight line path without friction. So option is correct in one situation only (which the question has not clearly specified) and is wrong in general. [a] This option clearly talks about the only possibility where a force may not be required. Moreover even if friction is considered the body continues its motion in straight line until velocity reduces to zero. Though to keep the body going along straight line a force is necessarily required to be applied on the body. Thus in option [b] force is not required in one situation. This situation is same in option [c] as well. But in option [c] there are many other situations, where a force is required. Hence option [b] is better. To keep the acceleration constant a net force is necessarily required.
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