Q: The potential energy of a particle varies with x according to the relation U(x) = x2 – 4 x. The point x = 2 is a point of :
(A) stable equilibrium
(B) unstable equilibrium
(C) neutral equilibrium
(D) none
Ans: (A)
Solution: U(x) = x2 – 4x
F = 0
$\frac{dU(x)}{dx} = 0 $
2 x – 4 = 0
x = 2
$\frac{d^2U(x)}{dx^2} = 2 > 0 $
i.e. U is minimum hence x = 2 is a point of stable equilibrium