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? *

Option 1: it doubles
Option 2: it quadruples
Option 3: it is cut in 1/2
Option 4: it is cut to 1/4
Option 5: stays unchanged

Answer 1

The acceleration of an object traveling in a circular path is inversely proportional to the radius. If the radius doubles and speed remains constant, the centripetal acceleration is cut to 1/4 of its original value.

Step-by-step explanation:

When an object travels at constant speed v in a circular path with radius r, it experiences centripetal acceleration (ac) directed towards the center of the circle. The formula for centripetal acceleration is ac = v2 / r, which shows that acceleration is proportional to the square of the speed and inversely proportional to the radius of the circle. Thus, if the radius is doubled (r becomes 2r) and the speed remains unchanged, the new acceleration (ac,new) would be ac / 2. Consequently, the acceleration is cut to 1/4 of the original value, making Option 4 the correct answer.