A ball balanced on a vertical rod is an example of
- (a)stable equilibrium
- (b)unstable equilibrium
- (c)neutral equilibrium
- (d)perfect equilibrium
Correct — B, unstable equilibrium. A ball perched on the tip of a vertical rod is balanced only so long as its centre of gravity sits exactly over the tiny area of contact. Nudge it by the smallest amount and the centre of gravity moves outside that support, gravity now exerts a turning effect in the direction of the nudge, and the ball rolls off instead of coming back. The test for the three kinds of equilibrium is what a small displacement does to the height of the centre of gravity: here it LOWERS it, potential energy falls, and the body keeps moving away from its original position. That is the definition of unstable equilibrium.
- (a)stable equilibrium — Stable equilibrium is the opposite case — a small push RAISES the centre of gravity, so gravity pulls the body back to where it started. A ball resting inside a bowl, or a cone standing on its base, behaves that way. A ball on a rod tip never returns.
- (c)neutral equilibrium — or a cone lying on its side. The ball on the rod does not stay put; it falls.
- (d)perfect equilibrium — There is no such category in mechanics. Equilibrium is classified as stable, unstable or neutral, and 'perfect' is an invented term put in to catch a guess.
A body is in equilibrium when the forces and the turning effects on it both add to zero. The three kinds differ only in what happens after a small disturbance. If the centre of gravity rises when the body is displaced, the body slides back down to its old position and the equilibrium is stable. If it falls, the body keeps going and the equilibrium is unstable. If it neither rises nor falls, the body rests in its new position and the equilibrium is neutral. Everyday stability follows from the same rule — a wide base and a low centre of gravity make a body hard to topple, which is why a racing car is built low and a double-decker bus carries its heavy engine underneath.
Classify by asking one question and one only: after a tiny push, does the centre of gravity go up, down or sideways at the same height? Standard examples worth memorising as a set are a ball, a cone on its side and a rolling cylinder for neutral. Note the physical detail that makes the rod case so delicate — the region of contact is essentially a point, so the vertical line through the centre of gravity must pass through that point exactly. A body with a broad base can be tilted quite far before the same line leaves the base, which is the difference between a wobble and a fall.
- Equilibrium requires zero net force and zero net turning effect on the body.
- Stable — a small displacement raises the centre of gravity and the body returns.
- Unstable — a small displacement lowers the centre of gravity and the body moves further away.
- Neutral — the centre of gravity stays at the same height and the body rests in the new position.
- A wide base and a low centre of gravity together make a body harder to topple.
One test settles all three cases: does a small displacement raise, lower or preserve the height of the centre of gravity?
- Assuming that because a body is balanced it must be in stable equilibrium; being balanced is the starting point, not the classification.
- Confusing neutral with stable — in neutral equilibrium the body neither returns nor runs away, it simply stays.
- Picking an invented category such as 'perfect equilibrium' when the three real ones are stable, unstable and neutral.
NDA gives a physical arrangement — a cone on its tip, a ball in a bowl, a pencil on its point — and asks for the class of equilibrium, or reverses it and asks for an example of a named class.
No directly related past PYQ was found.
- practice — not a real PYQ
A cone resting on its circular base is in
- (a)unstable equilibrium
- (b)neutral equilibrium
- (c)stable equilibrium
- (d)no equilibrium at all
Answer(c) stable equilibrium — tilting it raises the centre of gravity, so it settles back onto its base.
- practice — not a real PYQ
A body is in neutral equilibrium when, on being slightly displaced, its centre of gravity
- (a)rises
- (b)falls
- (c)stays at the same height
- (d)moves outside the body
Answer(c) stays at the same height — so the body simply remains in its new position, like a ball on a level table.