Question 289: Work, Energy and Power & Circular Motion

Question

A body performing uniform circular motion of radius 'R' has frequency 'n'. It centripetal acceleration is

Accepted Answer

The correct answer is
Option B: 4 $$\pi^2$$n$$^2$$R
.
Here's why:
Understanding Centripetal Acceleration
Centripetal acceleration is the acceleration that keeps an object moving in a circular path. It always points towards the center of the circle. The magnitude of centripetal acceleration (a
c
) is given by:
$$a_c = \frac{v^2}{R}$$
Where:
v is the object's speed
R is the radius of the circular path
Relating Frequency and Speed
Frequency (n) represents the number of revolutions the object completes per second. We can relate frequency to speed (v) as follows:
In one revolution, the object covers a distance equal to the circumference of the circle (2ÃÂR).  So, the speed is:
$$v = 2\pi Rn$$
Putting it Together
Substituting the expression for v in the centripetal acceleration formula, we get:
$$a_c = \frac{(2\pi Rn)^2}{R}$$
$$a_c = \frac{4\pi^2 R^2 n^2}{R}$$
$$a_c = \boxed{4\pi^2 n^2 R}$$
Therefore, the centripetal acceleration of a body performing uniform circular motion is 4ÃÂÃÂ²nÃÂ²R.

Answer

8 $$\pi^2$$nR$$^2$$

Answer

4 $$\pi^2$$n$$^2$$R

Answer

4 $$\pi^2$$n$$^2$$R$$^2$$

Answer

8 $$\pi^2$$n$$^2$$R

Work, Energy and Power & Circular Motion

A body performing uniform circular motion of radius 'R' has frequency 'n'. It centripetal acceleration is

Choose the correct answer: