WBJEE 2024 Physics & Chemistry Paper

Here we will use the concept of concavity of curves.
We know that,

F=‌

−dv

dx

Hence, when ‌

dv

dx

=0 or say the slope of v(x) vs x curve is zero, the net force is zero and we get an equilibrium point.
So, here in curve, points (1), (2) and (3) have slope equal to zero.
So, three equilibrium points.
Now, for stable equilibrium,
‌

d2v

dx2

>0

which should be a concave curve by concavity of curves.
Since, at point (2), the curve is in concave shape, so this is a stable equilibrium.
For unstable equilibrium,
‌

d2v

dx2

<0
By concavity of curves, unstable points should have a convex shape. Hence, we see points (1) and (2) are in unstable equilibrium. Therefore, option (C) is correct.