Question

In a uniform circular motion, radial acceleration is due to
A. Change in position of the particle along X-axis
B. Change in position of the particle along Y axis
C. Change in direction of tangential velocity
D. Change in magnitude of tangential velocity

Answer 1

Hint: You could begin with defining the term ‘acceleration’. Then you could express how acceleration is different for linear and circular motion. You could then think of how appropriate are each of the given options. Then you could recall the definition and then find the answer keeping in mind that we are dealing with uniform circular motion.

Complete step by step solution:
In the question, we are asked to find what causes the radial acceleration in a uniform circular motion in the given options.
We know that acceleration normally is defined as the time rate of change of speed. The motion can be linear or circular and each has their own respective acceleration related to them. The centripetal acceleration associated with circular motion can be resolved into radial and tangential components.
Now let us consider the given options. The first two options aren’t appropriate as we can draw the axes as per our wish and hence cannot be considered as a reference.
Now the motion under discussion is actually uniform circular motion which directly implies that the magnitude of the velocity remains the same.
So, we could conclude that the change in direction of the tangential velocity causes the radial acceleration. Hence, option C is the correct answer.

Note: The radial acceleration can be defined as the acceleration of the object undergoing circular motion that is directed along the radius of its trajectory. Mathematically the radial acceleration could be given by,
$a_r={\displaystyle \frac{v^2}{r}}$
Also, it is known to have the same unit as that of angular acceleration.