Answer:
The correct option is 'D': 9
Explanation:
We know that the magnitude of the centripetal acceleration of a body moving in circular orbit of radius 'r' with speed 'v' is given by
[tex]a_{c}=\frac{v^{2}}{r}[/tex]
Now when the speed of the body is tripled the speed becomes [tex]3v[/tex]
Hence the new centripetal acceleration is obtained as
[tex]a'_{c}=\frac{(3v)^{2}}{r}\\\\a'_{c}=\frac{9v^{2}}{r}=9a_{c}[/tex]
Thus we can see that the new centripetal acceleration becomes 9 times the oroginal value.
The acceleration of a body traveling in a circular route is known as centripetal acceleration. The magnitude of the centripetal acceleration increases by a factor of 9.
The acceleration of a body traveling in a circular route is known as centripetal acceleration. Because velocity is a vector quantity. It has both a magnitude and a direction.
When a body moves on a circular route, its direction changes constantly, causing its velocity to vary, resulting in acceleration.
Mathematically it is given as,
[tex]\rma_c=\frac{v^2}{r} \\\\ a_c'=\frac{(3v)^2}{r} \\\\ \rm v=9\frac{v^2}{r}\\\\ a_c'=9a_c[/tex]
Hence the magnitude of the centripetal acceleration increases by a factor of 9. Option c is correct.
To learn more about centripetal acceleration refer to the link;
https://brainly.com/question/17689540
