# An automobile drives over some hilly terrain. The motion of the automobile at the top of a hill is instantaneously similar to circular motion with the center of curvature beneath the road. The motion of the automobile at the bottom of a dip is instantaneously similar to circular motion with the center of curvature above the road. At any time there are three forces on the car: weight , normal  , and friction  of the tires with the road. The magnitudes of these three forces are given respectively by W, N, and f.(a) When the car is at the top of a hill, which of the following gives the magnitude of the centripetal force?(A) N                                    (B) W + N (C) W - N                              (D) N - W(b) When the car is at the bottom of a dip, which of the following gives the magnitude of the centripetal force?(A) N                                    (B) W + N (C) W - N                             (D) N – W

Kevin Nash
askIITians Faculty 332 Points
7 years ago
(a)
The figure below shows the normal force and the weight acting on the automobile on the top of a hill, and is equivalent to circular motion with the center of curvature beneath the road:

Thus, (C) is the correct option, while the rest are ruled out.
(b)
The figure below shows the normal force and the weight acting on the automobile on the bottom of a hill, and is equivalent to circular motion with the center of curvature above the road:

Thus, (D) is the correct option, while the rest are ruled out.