A small spherical body of mass M and density d₁ falls in a viscous liquid of density d₂ (where d₁ d₂ ). It eventually attains a uniform terminal velocity v₀ . The rate at which heat is dissipated by the viscous drag force is:

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A small spherical body of mass M and density d₁ falls in a viscous liquid of density d₂ (where d₁ > d₂ ). It eventually attains a uniform terminal velocity v₀ . The rate at which heat is dissipated by the viscous drag force is:

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Correct answer: D. Mg v₀ (1 - d₂ d₁ )

When the spherical body attains the uniform terminal velocity v₀ , the net force acting on it is zero. The forces acting on the body are its weight W downwards, the buoyant force B upwards, and the viscous drag force F_v upwards. W = B + F_v F_v = W - B The weight of the body is W = Mg . The volume of the body is V = M d₁ . The buoyant force is B = V d₂ g = ( M d₁ ) d₂ g = Mg ( d₂ d₁ ) . Substituting W and B into the equation for F_v : F_v = Mg - Mg ( d₂ d₁ ) = Mg (1 - d₂ d₁ ) The rate at which heat is dissipated b

A small spherical body of mass M and density d₁ falls in a viscous liquid of density d₂ (where d₁ > d₂ ). It eventually attains a uniform terminal velocity v₀ . The rate at which heat is dissipated by the viscous drag force is:

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