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NEET Physics: Equilibrium of rigid bodies Practice Questions

15 free multiple-choice questions on Equilibrium of rigid bodies (Rotational Motion) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.

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  1. Q1. For a body to be in rotational equilibrium, the net external torque acting on it about any point must be zero. If all forces are applied at the same point, the rotational equilibrium condition simplifies to:

    • ANet linear force must be zero
    • BThe resultant of all forces must be zero
    • CThe sum of forces must be zero
    • DThe net torque must be zero
    Show answer & explanation

    Correct answer: D — The net torque must be zero

    Rotational equilibrium is fundamentally defined by the balance of torques. If all forces are applied at a single point (the pivot or reference point), the position vector (r⃗) is zero, meaning the resulting torque (τ= r⃗ × F⃗) is automatically zero, regardless of the force magnitude.

  2. Q2. When a rigid body is in equilibrium, the condition for rotational equilibrium is defined by: (i) the net force acting on the body is zero. (ii) the net torque acting on the body is zero. (iii) the center of mass is stationary. (iv) the body is moving at a constant velocity.

    • A(i) and (iii) only
    • B(ii) only
    • C(i), (ii), and (iii)
    • D(i) and (ii) only
    Show answer & explanation

    Correct answer: D — (i) and (ii) only

    For a body to be in complete equilibrium (both translational and rotational), both the net force (ΣF=0) and the net torque (Στ=0) must be zero. While ΣF=0 implies Στ=0 if applied correctly, the fundamental condition for rotational equilibrium is Στ= 0.

  3. Q3. A body is subjected to an external torque. If the body is already in equilibrium, what must happen to the applied torque for it to remain in equilibrium?

    • AThe torque must be perpendicular to the axis of rotation only.
    • BThe torque must be opposite to the net linear force.
    • CThe torque must be equal to the moment of inertia.
    • DThe torque must be zero.
    Show answer & explanation

    Correct answer: D — The torque must be zero.

    For equilibrium, the net torque must be zero. If an external torque is applied, the body will only remain in equilibrium if the applied torque is zero, or if an equal and opposite torque exists, thus resulting in a net zero torque.

  4. Q4. A rigid body is in equilibrium when the net external torque acting on it is zero. What physical quantity is directly proportional to the net external torque?

    • AForce
    • BAngular Velocity
    • CAngular Momentum
    • DLinear Momentum
    Show answer & explanation

    Correct answer: C — Angular Momentum

    Torque (τ) is defined as the rotational equivalent of force, and it is directly proportional to the angular momentum change or, in terms of acceleration, proportional to the angular acceleration (τ= Iα).

  5. Q5. If a body is in equilibrium, the net external force acting on the body must be zero. This condition is necessary for which type of equilibrium?

    • AAngular acceleration equilibrium
    • BRotational equilibrium
    • CDynamic equilibrium
    • DTranslational equilibrium
    Show answer & explanation

    Correct answer: D — Translational equilibrium

    For any body, both translational equilibrium (ΣF = 0) and rotational equilibrium (Στ= 0) must be satisfied for static equilibrium.

  6. Q6. The moment of inertia of a circular ring of mass M and radius R about its center is:

    • AMR³
    • BMR²
    • CM/R²
    • DMR
    Show answer & explanation

    Correct answer: D — MR

    The moment of inertia (I) of a ring about its center is given by I = MR².

  7. Q7. A uniform rigid bar is held in equilibrium by two forces acting at its ends. If the forces are applied symmetrically, what is the condition for the bar to be in rotational equilibrium?

    • AThe net force must be zero.
    • BThe magnitude of the forces must be equal.
    • CThe perpendicular distance between the forces must be zero.
    • DThe net torque about any point must be zero.
    Show answer & explanation

    Correct answer: D — The net torque about any point must be zero.

    For a rigid body to be in rotational equilibrium, the net external torque (Στ) acting on it must be zero. This is the fundamental condition for rotational equilibrium.

  8. Q8. Which of the following statements correctly describes the condition for rotational equilibrium of a rigid body?

    • AThe net torque acting on the body must be zero.
    • BThe body must be rotating at a constant angular speed.
    • CThe net force acting on the body must be zero.
    • DThe net angular momentum must be conserved.
    Show answer & explanation

    Correct answer: A — The net torque acting on the body must be zero.

    Rotational equilibrium requires that the rotational analogue of Newton's first law holds, which is that the net external torque acting on the body must be zero.

  9. Q9. Two forces acting on a body produce equal and opposite torques. What is the state of rotational motion of the body?

    • AThe body is undergoing angular acceleration
    • BThe body is accelerating rotationally
    • CThe body is rotating at a constant rate
    • DThe body is in equilibrium (or rotating at constant angular velocity)
    Show answer & explanation

    Correct answer: D — The body is in equilibrium (or rotating at constant angular velocity)

    If the net external torque is zero (equal and opposite torques), the body is either in equilibrium or rotating with constant angular velocity (zero angular acceleration).

  10. Q10. If the net external torque acting on a rigid body is zero, what does this imply about its rotational motion?

    • AThe body is in rotational equilibrium (at rest or constant rotation).
    • BThe body is undergoing angular acceleration.
    • CThe body is rotating at a constant angular velocity.
    • DThe body is undergoing angular deceleration.
    Show answer & explanation

    Correct answer: A — The body is in rotational equilibrium (at rest or constant rotation).

    Zero net torque implies that there is no change in rotational motion, meaning the body is either at rest or rotating at a constant angular velocity (rotational equilibrium).

  11. Q11. Which statement correctly describes the condition for static equilibrium of a rigid body?

    • AThe net force is zero and the net torque is non-zero.
    • BThe net force is non-zero and the net torque is zero.
    • CThe net force is zero and the net torque is zero.
    • DThe net force is non-zero and the net torque is non-zero.
    Show answer & explanation

    Correct answer: C — The net force is zero and the net torque is zero.

    Static equilibrium requires both the linear forces to balance (ΣF = 0) and the rotational forces to balance (Στ= 0).

  12. Q12. Two equal and opposite forces of magnitude F act on a rigid body at the same point, producing zero net external torque. Which statement is true regarding the state of rotation of the body immediately after these forces are applied?

    • AThe body is in rotational equilibrium (no angular acceleration).
    • BThe body is accelerating rotationally in the direction of the larger force.
    • CThe body is undergoing angular acceleration in the direction opposite to the net force.
    • DThe body is in translational equilibrium but rotating at a constant angular velocity.
    Show answer & explanation

    Correct answer: A — The body is in rotational equilibrium (no angular acceleration).

    For rotational equilibrium, the net external torque (τₙₑₜ) must be zero. If two equal and opposite forces act at the same point, they produce zero net torque. This condition implies that the body is in rotational equilibrium, meaning its angular velocity does not change (or it is at rest).

  13. Q13. A body is in equilibrium under the action of three forces, F₁ = 10 N, F₂ = 5 N, and F₃ = 12 N. What is the condition for the net torque acting on the body to be zero?

    • AF₁ × F₂ = F₃
    • BF₁ + F₂ + F₃ = 0
    • CΣτ= 0
    • DThe forces must be collinear
    Show answer & explanation

    Correct answer: C — Στ= 0

    For a body to be in rotational equilibrium, the net external torque acting on it must be zero (Στ= 0). This is the fundamental condition for rotational equilibrium.

  14. Q14. The quantity used to measure the rotational equivalent of force is called torque. Which of the following is the SI unit of torque?

    • ANewton-meter (N·m)
    • BNewton (N)
    • CKilogram (kg)
    • DJoule (J)
    Show answer & explanation

    Correct answer: A — Newton-meter (N·m)

    Torque is calculated as Force times perpendicular distance (Force × distance), so its unit is Newton-meter (N·m).

  15. Q15. A force F is applied to a rigid body at a distance r from the axis of rotation, causing a torque of F · r. If the net external torque acting on the body is zero, what must be true about the relationship between the applied forces and their distances from the axis?

    • AThe sum of the torques produced by all forces must be zero, regardless of their direction.
    • BThe magnitudes of the torques produced by forces must balance, meaning Σ(Fᵢ rᵢ) = 0.
    • CThe forces must be perpendicular to the radius vector to achieve equilibrium.
    • DAll applied forces must be equal in magnitude and directed along the same line.
    Show answer & explanation

    Correct answer: B — The magnitudes of the torques produced by forces must balance, meaning Σ(Fᵢ rᵢ) = 0.

    Rotational equilibrium requires Στ= 0. Since torque is calculated as τ= F r sin θ, for the net torque to be zero, the vector sum of the torques must balance. If we consider only torques due to forces perpendicular to the position vector (or simplifying to the magnitude condition), the condition for equilibrium is that the algebraic sum of the individual torques is zero: Σ(Fᵢ rᵢ) = 0.

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