An object travels in a circular path of radius r at a constant speed v. What happens to the object’s acceleration if the radius of the circle is doubled and the speed stays unchanged? A. It doubles B. It quadruples C. It is cut to a half
Question
An object travels in a circular path of radius r at a constant speed v. What happens to the object’s acceleration if the radius of the circle is doubled and the speed stays unchanged? A. It doubles B. It quadruples C. It is cut to a half
Solution
The acceleration of an object moving in a circular path is given by the formula a = v^2 / r, where v is the speed and r is the radius of the circle. If the radius is doubled and the speed remains unchanged, the new acceleration a' = v^2 / 2r.
Comparing the new acceleration a' with the original acceleration a, we see that a' = a / 2. Therefore, the acceleration is cut to a half when the radius of the circle is doubled and the speed stays unchanged. So, the correct answer is C. It is cut to a half.
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