For a particle in a non- uniform accelerated circular motiona)Velocity...
Explanation:
Non-uniform circular motion is the motion of an object moving in a circular path with a varying speed. The direction of the velocity and acceleration of an object in non-uniform circular motion changes at every point on the circular path.
Velocity:
Velocity is the rate of change of displacement with respect to time. In non-uniform circular motion, the velocity of the object is always tangent to the circular path. The magnitude of the velocity changes at every point on the circular path.
Acceleration:
Acceleration is the rate of change of velocity with respect to time. In non-uniform circular motion, the acceleration of the object is not constant. It changes at every point on the circular path.
Now, let's discuss the given options one by one:
a) Velocity is radial and acceleration is transverse only:
In this option, the velocity is radial which means it is directed towards the center of the circular path. But the acceleration is transverse which means it is perpendicular to the velocity vector. This option is correct because the direction of the acceleration is always towards the center of the circular path in non-uniform circular motion.
b) Velocity is transverse and acceleration is radial only:
In this option, the velocity is transverse which means it is perpendicular to the radius vector. But the acceleration is radial which means it is directed towards the center of the circular path. This option is incorrect because the direction of the acceleration is not always radial in non-uniform circular motion.
c) Velocity is radial and acceleration has both radial and transverse components:
In this option, the velocity is radial which means it is directed towards the center of the circular path. But the acceleration has both radial and transverse components. This option is incorrect because the direction of the acceleration is always towards the center of the circular path in non-uniform circular motion.
d) Velocity is transverse and acceleration has both radial and transverse components:
In this option, the velocity is transverse which means it is perpendicular to the radius vector. But the acceleration has both radial and transverse components. This option is incorrect because the direction of the acceleration is not always radial in non-uniform circular motion.
Hence, the correct option is 'a' - Velocity is radial and acceleration is transverse only.
For a particle in a non- uniform accelerated circular motiona)Velocity...
Since the acceleration is non-uniform, acceleration has radial component due to centripetal force, as well as a transverse component. While the velocity has a transverse component only whose magnitude is not constant.
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