Question

The potential energy of a particle varies with x according
to the relation U(x)=x2-4x. The point x = 2 is a point of
(1) stable equilibrium
(2) unstable equilibrium
(3) neutral equilibrium
(4) none of above​

Answer 1

Answer:

neutral equilibrium.....

hope it's write

Answer 2

The point x = 2 is a point of stable equilibrium

• The potential energy of a particle varies with x according to the relation

$U(x)=x {}^{2} -4x$

• We know that,

$F = - dU/dx$

$dU/dx = 2x - 4$

• At x = 2

$dU/dx = 2×2 - 4$

$dU/dx = 0$

And,

$d {}^{2} U /dx {}^{2} = 2$

$d {}^{2} U/dx {}^{2} > 0$

• This condition is for stable equilibrium.