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NEET 2018 · Viscosity & Stokes' Law

Viscosity & Stokes' Law question from NEET 2018

Q29NEET 2018Medium

Viscosity & Stokes' Law

A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

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Answer: (c)

  1. Rate of heat production = power of viscous force: P=Fvt=6πηrvt2P = F v_t = 6\pi\eta r v_t^2.
  2. Terminal velocity vt=2r2(ρ−σ)g9η∝r2v_t = \frac{2r^2(\rho-\sigma)g}{9\eta} \propto r^2.
  3. P∝r⋅(r2)2=r5P \propto r\cdot(r^2)^2 = r^5
  4. So the answer is (c) r5r^5.
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