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Exam level5 past questions

Circular motion and centripetal force

Analyze the forces involved in uniform and non-uniform circular motion, including centripetal force, tension, and friction.

Why this shows up in the exam

NEET tests your understanding of how forces act in circular paths, especially in practical contexts like vehicles on roads.

How NEET tests this

Numerical · 3 QsApplication · 2 QsDirect recall

Learn the idea

Centripetal force is the inward force needed to keep a body moving in a circle; any tension, friction or normal force that supplies F=mv²/r (or mω²r) is the centripetal force. The key insight is that the required force varies with the square of the speed (or angular speed).

🧠 Memory hook: C = C for Curve, square the speed, divide by radius – C ∝ v²/r

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

Formulas & facts to keep ready

  • Centripetal force F_c = mv²/r
  • Centripetal force also F_c = mω²r where ω = v/r
  • For a body on a horizontal curve, friction provides F_c ≤ μmg → v_max = √(μg r)
  • Angular speed in rad/s = (2π × rpm)/60
  • Tension in a horizontal string = mω²r, so T ∝ ω²
  • In a vertical circle the minimum speed at the top is √(g r) to keep the string taut

How to approach it

  1. 1Identify the source of the centripetal force (tension, friction, normal, etc.)
  2. 2Write the appropriate expression F_c = mv²/r or F_c = mω²r
  3. 3Replace v by ωr if angular speed is given, and convert rpm to rad/s when needed
  4. 4Solve for the unknown (speed, tension, height, etc.) using algebra

Worked example — watch it click

A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm. The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes:

  • A)T/4
  • B)√2T
  • C)T
  • ✅4T

The concept behind this problem

The example checks whether you remember that tension supplies the centripetal force and that doubling the angular speed quadruples the required tension because T ∝ ω².

Step by step

  1. 1For circular motion in a horizontal plane, centripetal force is provided by tension: T = mω²r, where ω is angular velocity in rad/s.
  2. 2Given initial angular speed ω rpm corresponds to angular velocity ω₁ = (ω × 2π)/60 rad/s.
  3. 3When speed becomes 2ω rpm, angular velocity ω₂ = (2ω × 2π)/60 = 2ω₁.
  4. 4Since T ∝ ω², the new tension T' = m(ω₂)²r = m(2ω₁)²r = 4m(ω₁)²r = 4T.

Watch out

Most students think the tension doubles when the speed doubles, overlooking the square relationship.

Common slip-ups that cost marks

  • •Forgetting to convert rpm to rad/s before squaring
  • •Using μg instead of μg r when the question asks for speed, not acceleration
  • •Assuming tension changes linearly with speed instead of with the square of speed

🌟 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 motorcycle is travelling on a curved track of radius 500 m if the coefficient of friction between road and tyres is 0.5. The speed for avoiding skidding will be:

Push further

More challenging

5 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 5

A simple pendulum of length 'l' is oscillating in a liquid of density 'ρ_L'. The bob has a mass 'm' and density 'ρ_B'. What is the time period of oscillation?

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