A particle is moving in a uniform circular motion with constant speed v along a circle of radius r. The acceleration of the particle is
A. zero
B. $$\frac{v}{r}$$
C. $$\frac{v}{{{r^2}}}$$
D. $$\frac{{{v^2}}}{r}$$
Answer: Option D
Solution (By Examveda Team)
The question is asking about the acceleration of a particle moving in a circle at a constant speed.Important Point: Even though the speed is constant, the velocity isn't! Velocity includes both speed AND direction. Since the particle is moving in a circle, its direction is constantly changing.
Because the direction is changing, the particle is accelerating. This acceleration is called centripetal acceleration, and it always points towards the center of the circle.
Now, the formula for centripetal acceleration is:
a = v2 / r
Where:
* a is the centripetal acceleration
* v is the speed of the particle
* r is the radius of the circle
So, let's look at the options:
Option A: zero - Incorrect because we know there *is* acceleration.
Option B: v/r - Incorrect. This is not the correct formula.
Option C: v/r2 - Incorrect. This is not the correct formula.
Option D: v2/r - Correct! This matches the formula for centripetal acceleration.
Therefore, the answer is D. The acceleration of the particle is v2/r.
This Question Belongs to Physics GK Chapter Wise >> Law Of Motion
In uniform circular motion, even though the speed is constant, the velocity is changing due to the continuous change in direction. This change in direction results in an acceleration called centripetal acceleration.
The formula for centripetal acceleration is:
a = rac{v^2}{r}
= speed of the particle
= radius of the circular path
So, the correct answer is D. v² / r.