What will happen to the centripetal acceleration if the radius of a circular path is halved while maintaining the speed?

The formula for centripetal acceleration is given by ( a_c = \frac{v^2}{r} ), where ( a_c ) is the centripetal acceleration, ( v ) is the speed of the object moving in a circular path, and ( r ) is the radius of that path.

When the radius ( r ) is halved and the speed ( v ) remains constant, we can substitute ( r/2 ) into the equation for centripetal acceleration:

[

a_c' = \frac{v^2}{r/2} = \frac{v^2}{(1/2)r} = \frac{2v^2}{r}

]

This shows that the new centripetal acceleration ( a_c' ) is twice the original centripetal acceleration ( a_c ). Therefore, reducing the radius to half results in the centripetal acceleration doubling, so the correct outcome is that it does not halve, remains the same, or quadruple.

Consequently, if the radius of the circular path is halved while maintaining speed, the centripetal acceleration will double.