Two solid spherical balls of radius r1 & r2 (r2 < r1) and density σ are tied up with a string and released in a viscous liquid of lesser density ρ and coefficient of viscosity η, with the string just taut as shown. The terminal velocity of the spheres is:
Correct answer: C. Option C: vt = (2/9) * (σ - ρ) * g * (r1² + r2²) / (2 * η)
- A. Option A: vt = (2/9) * (σ - ρ) * g * r1² / η
- B. Option B: vt = (2/9) * (σ - ρ) * g * r2² / η
- C. Option C: vt = (2/9) * (σ - ρ) * g * (r1² + r2²) / (2 * η)
- D. Option D: vt = (4/9) * (σ - ρ) * g * r1 * r2 / η
Explanation
The correct answer is Option C. Since the two spheres are tied together and moving through a viscous fluid, their terminal velocity depends on the combined effect of their radii. The terminal velocity formula for a sphere moving through a viscous fluid is modified to account for both spheres. At terminal velocity net force is zero.6πη(r₁+r₂)V┬+⅔π(r₁³+r₂³)ρg = ⅔π(r₁³+r₂³)σgOption A and Option B are incorrect as they only consider one sphere each, ignoring the connection between them. Option D incorrectly combines the radii, which does not reflect the physics of the situation.
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