n object of mass m moves at a constant speed v around a circular path of radius r. The net force applied on the object is F. What happens to the net force if speed is doubled and radius is quadrupled? A. It doubles B. It quadruples C. Stays the same D. It is cut to one-half E. It is cut to one-quarter
Question
n object of mass m moves at a constant speed v around a circular path of radius r. The net force applied on the object is F. What happens to the net force if speed is doubled and radius is quadrupled? A. It doubles B. It quadruples C. Stays the same D. It is cut to one-half E. It is cut to one-quarter
Solution
The net force applied on an object moving in a circular path is given by the centripetal force formula:
F = mv²/r
where: m = mass of the object v = speed of the object r = radius of the circular path
If the speed is doubled, the new speed becomes 2v. If the radius is quadrupled, the new radius becomes 4r. Substituting these into the formula gives the new force F':
F' = m(2v)²/(4r) = 4mv²/4r = mv²/r = F
So, the net force stays the same. The answer is C. Stays the same.
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