Types of Equilibrium — NEET Physics MCQs with Solutions
Free NEET Physics Types of Equilibrium MCQs with step-by-step solutions (8 questions). Part of Work, Power and Energy. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Types of Equilibrium · easy · theory
In STABLE equilibrium, the potential energy of the body is at a:
A. Constant value everywhere
B. Minimum ✓ Correct
C. Maximum
D. Point of inflection
Solution: Stable: U minimum (displacement raises U, restoring force pulls back). Unstable: U maximum. Neutral: U constant.
Q2 — Types of Equilibrium · medium · theory
The mathematical conditions for STABLE equilibrium at x₀ are:
A. dU/dx > 0
B. d²U/dx² = 0 only
C. dU/dx = 0 and d²U/dx² < 0
D. dU/dx = 0 and d²U/dx² > 0 ✓ Correct
Solution: Equilibrium needs zero force (dU/dx = 0); a positive second derivative makes it a minimum ⇒ stable.
Q3 — Types of Equilibrium · easy · numerical
For U(x) = x² (J), the equilibrium at x = 0 is:
A. Unstable
B. Stable ✓ Correct
C. Neutral
D. Not an equilibrium
Solution: dU/dx = 2x = 0 at x = 0; d²U/dx² = 2 > 0 ⇒ minimum ⇒ stable (this is the spring potential).
Q4 — Types of Equilibrium · medium · numerical
For U(x) = x³ − 3x (J), the STABLE equilibrium position is:
A. x = 0
B. x = ±√3
C. x = +1 m ✓ Correct
D. x = −1 m
Solution: dU/dx = 3x² − 3 = 0 ⇒ x = ±1. d²U/dx² = 6x: positive at x = +1 (stable), negative at x = −1 (unstable).
Q5 — Types of Equilibrium · hard · numerical
For U(x) = x⁴/4 − x²/2 (J), the stable equilibrium positions are:
A. x = ±2
B. None exist
C. x = ±1 (x = 0 is unstable) ✓ Correct
D. x = 0 only
Solution: dU/dx = x³ − x = 0 ⇒ x = 0, ±1. d²U/dx² = 3x² − 1: at 0 it is −1 (max, unstable); at ±1 it is +2 (minima, stable) — a double-well potential.
Q6 — Types of Equilibrium · medium · numerical
For U(x) = 2x³ − 6x (J), the equilibrium at x = +1 m is:
A. Not an equilibrium point
B. Neutral
C. Stable ✓ Correct
D. Unstable
Solution: dU/dx = 6x² − 6 = 0 at x = ±1; d²U/dx² = 12x = +12 > 0 at x = 1 ⇒ U minimum ⇒ stable.
Q7 — Types of Equilibrium · easy · numerical
For U(x) = 5 + (x − 1)² (J), the stable equilibrium is at:
A. x = 1 m ✓ Correct
B. x = −1 m
C. x = 5 m
D. x = 0
Solution: U is a parabola with minimum at x = 1 (U = 5 J there); F = −2(x−1) is restoring about it.
Q8 — Types of Equilibrium · medium · theory
A cylinder lying on its curved side on a horizontal table is in ______ equilibrium:
A. Unstable
B. Neutral ✓ Correct
C. Stable
D. No equilibrium
Solution: Rolling it sideways neither raises nor lowers its centre of gravity ⇒ U constant ⇒ neutral. (On its flat end: stable; balanced on an edge: unstable.)