A rod is balanced vertically on one of its ends. Which one among the following is the correct nature of its state of equilibrium?

The correct answer is C, Unstable equilibrium. A rod standing upright on one end falls over at the slightest push, because its centre of gravity is high and its base is tiny. A body is in unstable equilibrium when a small displacement raises no restoring force and instead lowers its centre of gravity, so it moves further away from its first position. The upright rod is the textbook example: once it tilts, the line through its centre of gravity falls outside the narrow base, the weight produces a turning effect and the rod topples. Laid flat on the ground, the same rod would be in stable or neutral equilibrium. Option A is wrong because neutral equilibrium needs the centre of gravity to stay at the same height when the body moves, as with a ball on a level floor. Option B is wrong because a stable body returns to its position, as a cone resting on its base does. Option D is wrong because it is not a standard type of equilibrium. Exam tip: cone on base is stable, cone on tip is unstable, cone on its side is neutral.