Question

Assertion: In a uniform circular motion, the angle between velocity vector and acceleration vector is always$\dfrac{\pi }{2}$.
Reason: For any type of motion, the angle between acceleration and velocity is always$\dfrac{\pi }{2}$.
A. Both assertion and reason are correct and reason is the correct explanation for assertion.
B. Both assertion and reason are correct and reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect.
D. Assertion is incorrect but reason is correct.

Answer 1

To solve the above question we will first find whether the angle between the acceleration vector and velocity vector of uniform circular motion is $\dfrac{\pi }{2}$and if it is same for other types of motions too. So, we will first discuss what is the relationship between the acceleration and velocity vector?

Complete answer:
To find the answer to the above question where we have to find whether the angle between the velocity vector and acceleration vector is always $\dfrac{\pi }{2}$or not also we have to find that if any type of motion has the angle as $\dfrac{\pi }{2}$between its acceleration and velocity vector.
So, let us first discuss uniform circular motion and what is the relation between acceleration and velocity?
When an object rotates about an axis, like we can say with a tire of a car or a record rotating on a turntable, the motion can be described in two ways that is the point on the edge of the rotating object will have some velocity and will be carried through an arc by riding the spinning object. The point will travel through a distance of $\Delta S$. The amount the object rotates is called the rotational angle and can be measured in either degrees or radians. Since the rotational angle is related to the distance $\Delta S$ and to the radius r. It is usually more convenient to use radians.
In a uniform circular motion, velocity is along tangential direction and acceleration is always towards center, so angle between velocity vector and acceleration vector is always π/2. But in general, the angle between velocity and the acceleration can be acute or obtuse also.
So, we can say that option (C) is correct because the assertion is correct that the angle between acceleration vector and velocity of uniform circular motion is$\dfrac{\pi }{2}$, but it is not always for all types of motion. So, the reason is not correct.

Note: The magnitude of tangential acceleration is the rate of change of the magnitude of the velocity with respect to time. The tangential acceleration vector is tangential to the circle, whereas the centripetal acceleration vector points radially inward toward the center of the circle. The total acceleration is the vector sum of tangential and centripetal accelerations.