Skip to content
Activity 1.3.4 · Q1

Q.A stone is tied to a string and whirled such that the stone performs horizontal circular motion. It can be seen that the string is NEVER horizontal.

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
23% · 25/108 Questions
✓ Free question

Whirling faster only brings the string CLOSER to horizontal — it can never get there.

The whirled stone is a conical pendulum: tension T0T_0 resolves into T0cos⁡θT_0\cos\theta (vertical, balancing mg) and T0sin⁡θT_0\sin\theta (horizontal, the centripetal force). Since T0cos⁡θ=mgT_0\cos\theta = mg must always hold, cos⁡θ\cos\theta can never be zero — i.e. θ < 90° strictly. Pushing θ towards 90° forces T0=mg/cos⁡θ→∞T_0 = mg/\cos\theta \to \infty and, from n=12πg/(Lcos⁡θ)n = \frac{1}{2\pi}\sqrt{g/(L\cos\theta)}, an infinite frequency with zero period — along with infinite kinetic energy — all physically impossible. The faster you whirl, the closer the string rises towards horizontal, but it always keeps a finite droop.

✓Final answer

Because T0cos⁡θT_0\cos\theta must equal mg, the string must always keep a nonzero vertical inclination — it is NEVER horizontal.

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.