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Exam level5 past questions

Torque and rotational equilibrium

Torque is the rotational analogue of force, causing angular acceleration, and equilibrium occurs when the net torque on a body is zero.

Why this shows up in the exam

NEET often asks you to analyze situations involving torques, rotational equilibrium, and the principle of moments.

How NEET tests this

Numerical · 4 QsApplication · 2 QsDirect recall

Learn the idea

Torque is the vector product τ = r × F; rotational equilibrium means the vector sum of all torques on a body is zero. The key insight is that τ is always perpendicular to both r and F, so any dot product with r or F vanishes.

🧠 Memory hook: Think of a screwdriver: the handle (r) twists the screw (F) only when they are at right angles – that twist is the torque.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • τ = r × F (vector product)
  • |τ| = r F sinθ, where θ is the angle between r and F
  • Direction of τ given by right‑hand rule
  • Rotational equilibrium: Στ = 0 (vector sum)
  • Principle of moments: clockwise moments = anticlockwise moments about any axis
  • r·τ = 0 and F·τ = 0 always

How to approach it

  1. 1Identify the pivot (or axis) about which torques are to be taken
  2. 2Write each torque as τ = r × F or as magnitude r F sinθ with appropriate sign
  3. 3Add all torques vectorially (or use scalar moments about the chosen axis) and set Στ = 0
  4. 4Use the perpendicular property (r·τ = 0, F·τ = 0) to simplify calculations

Worked example — watch it click

If F is the force acting on a particle having position vector r and τ is the torque of this force about the origin, then :

  • A)r.τ > 0 and F.τ < 0
  • ✅r.τ = 0 and F.τ = 0
  • C)r.τ = 0 and F.τ ≠ 0
  • D)r.τ ≠ 0 and F.τ = 0

The concept behind this problem

The example checks whether you remember that τ = r × F is orthogonal to both r and F, so their dot products must be zero.

Step by step

  1. 1Torque τ = r × F.
  2. 2By properties of cross product: r · τ = r · (r × F) = 0 (always perpendicular).
  3. 3Similarly, F · τ = F · (r × F) = 0.
  4. 4Both dot products are zero regardless of r and F.

Watch out

Treating τ as a scalar magnitude leads to the mistaken belief that r·τ or F·τ could be non‑zero.

Common slip-ups that cost marks

  • •Ignoring the perpendicular distance – use the shortest distance from the line of action to the pivot
  • •Mixing up sign convention for clockwise and anticlockwise moments
  • •Assuming a force whose line of action passes through the pivot produces torque (it does not)

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 5

A uniform meter scale balances horizontally on a knife edge placed at 55 cm mark. When a mass of 25 g is supported from one end, then the mass of the scale is

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