Question

In uniform circular motion, the velocity vector and acceleration vector are:
A. perpendicular to each other
B. in the same direction
C. opposite in direction
D. not related to each other

Answer 1

We know that when a body is moving in a circular motion, it has two accelerations associated with it, one is tangential acceleration, and the other is radial acceleration. The resultant acceleration is given by the combined effect of radial as well as tangential acceleration.

Complete step by step answer: It is given that the body is performing the circular motion, and it is uniform in nature. We know that the uniform motion speed of the body is not changing as time progresses. The velocity of a body at a point when it is in a circular motion is tangentially outward, the direction of velocity is changing at every instant so we can say that velocity is changing with respect to time.

From the concept of uniform motion, we can say that the value of tangential acceleration is zero, so there is only one acceleration left for us that is radial. We know that the direction of radial acceleration is always towards the centre of the circular path. As radial acceleration is towards the centre and velocity is tangent to the circle at every point.

Therefore, based on the above explanation, we can conclude that the vector of velocity and acceleration are perpendicular to each other, and option (A) is correct.

Note: We can note that the direction of radial acceleration is along the radius and always towards the centre, the direction of velocity is changing at every instant, but the angle between these two is always constant and equal to a right angle.