KCSE 2025 Physics P1 Q8 — Unstable Equilibrium of an Upright Oval Ball
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The Question
“An oval ball is balanced standing on its end on the ground. Explain why it is in unstable equilibrium.”
Note the starting position
Balanced upright on its end, the ball rests on a tiny point of contact with the ground and its centre of gravity sits high up, directly above that small base. The line of action of the weight passes exactly through the point of contact, so for the instant it is balanced.
Give it a small displacement
Tip the ball slightly and the centre of gravity swings sideways so that its line of action falls outside the small base. In doing so the centre of gravity actually drops to a lower position than when the ball stood upright. The weight now acts through a line that misses the point of contact.
Follow the turning moment
With the weight acting outside the base, it sets up a turning moment about the point of contact. That moment does not restore the ball — it rotates it further from the upright position, so the ball topples over and cannot return on its own.
Final Result
It is in unstable equilibrium because the slightest displacement lowers the centre of gravity and moves its line of action outside the small base, so the weight produces a turning moment that carries the ball further from its original position instead of restoring it.
Why this method works
The type of equilibrium is decided by what happens to the centre of gravity during a small displacement. If a nudge raises the centre of gravity, gravity pulls the body back and the equilibrium is stable; if the height is unchanged it is neutral; and if the nudge lowers the centre of gravity the body keeps moving in the direction of the push, which is unstable. An oval ball on its end has its centre of gravity perched as high as it can be over a minute base, so any displacement can only send that centre of gravity downward. The resulting weight moment then acts to increase the displacement rather than cancel it, which is precisely the definition of unstable equilibrium.
Contrast it with the same ball lying on its side: a nudge there raises the centre of gravity, gravity restores it, and that position is stable.