[amp_mcq option1=”$$\frac{{\text{r}}}{{{{\text{v}}^2}}}$$” option2=”$$\frac{{{{\text{v}}^2}}}{{\text{r}}}$$” option3=”$$\frac{{\text{r}}}{{{\omega ^2}}}$$” option4=”$$\frac{{{\omega ^2}}}{{\text{r}}}$$ E. $${\text{r}}\omega $$” correct=”option1″]
The correct answer is $\boxed{\frac{{{{\text{v}}^2}}}{{\text{r}}}}$.
Centripetal acceleration is the acceleration of an object towards the center of a circle that it is moving in. It is always directed towards the center of the circle, and its magnitude is given by the formula:
$$a_c = \frac{v^2}{r}$$
where $v$ is the linear velocity of the object and $r$ is the radius of the circle.
Linear velocity is the rate at which an object changes its position. It is given by the formula:
$$v = \frac{ds}{dt}$$
where $ds$ is the change in position and $dt$ is the change in time.
Angular velocity is the rate at which an object rotates. It is given by the formula:
$$\omega = \frac{d\theta}{dt}$$
where $\theta$ is the angle through which the object rotates and $dt$ is the change in time.
The relationship between linear velocity and angular velocity is given by the formula:
$$v = r\omega$$
where $r$ is the radius of the circle.
Substituting this into the formula for centripetal acceleration, we get:
$$a_c = \frac{(r\omega)^2}{r} = \omega^2$$
Therefore, the centripetal acceleration of a moving body along the circular path of radius $r$ is $\boxed{\frac{{{{\text{v}}^2}}}{{\text{r}}}}$.
The other options are incorrect because they do not take into account the radius of the circle.