Question

The potential energy of a particle varies with position x according to the relation   2 U x 4x x   . The point x = 2 is a point of 1) stable equilibrium 2) unstable equilibrium 3) neutral equilibrium 4) none of the above

Answer 1

Answer:

Explanation:

Taking 2nd derivative

Stable ------ +ve

Unstable ----  -ve

Neutral  ------ 0

Here

1st derivative is

du /dx = 2x -4

2nd derivative is

2 which is +ve

Answer 2

Answer:

Explanation

U(x) = X2 - 4X

F =0

dU(x)/dx =0

2x -4 =0 x=2

d2U/dx2 = 2 ← 0

I.e. U is minimum hence

x=2 is a point of stable equilibrium