A ball attached to the end of a string is swung around in a circular path of radius r.If the radius is doubled and the linear speed is kept constant,
A)the centripetal acceleration remains the same.
B)the centripetal acceleration increases by a factor of 2.
C)the centripetal acceleration decreases by a factor of 2.
D)the centripetal acceleration increases by a factor of 4.
E)the centripetal acceleration decreases by a factor of 4.

Question

Quizplus · Accepted Answer

The centripetal acceleration is given by a = v^2/r where v is the linear velocity and r is the radius of the circular path. If the radius is doubled while the velocity is kept constant, then the centripetal acceleration decreases by a factor of 2. This can be seen from the equation, where the numerator (v^2) remains constant, but the denominator (r) doubles, leading to a decrease in the acceleration by a factor of 2. Therefore, the correct choice is C, the centripetal acceleration decreases by a factor of 2.

A Ball Attached to the End of a String Is