Question

question 9.
an object moves in a circular path at a constant speed. if the radius of the circle is doubled while the speed remains the same, how does the centripetal acceleration change?
a) it doubles
b) it stays the same
c) it becomes four times larger
d) it becomes half as large

Explanation:

Step1: Write the formula for centripetal acceleration

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

Step2: Analyze the change when radius is doubled

Let the initial radius be \(r_1 = r\) and the final radius be \(r_2=2r\). The initial centripetal acceleration \(a_{c1}=\frac{v^2}{r}\). The final centripetal acceleration \(a_{c2}=\frac{v^2}{2r}\).
We can see that \(a_{c2}=\frac{1}{2}a_{c1}\)

Answer:

d) It becomes half as large