Physics · Viscosity, Stoke's law, terminal velocity, streamline and turbulent flow, critical velocity
Eight drops of a liquid of density and each radius a are falling through air wit
Eight drops of a liquid of density \( \rho \) and each radius a are falling through air with a constant velocity \( 3.75 \mathrm{cm} s^{-1} \) when the eight drops coalesce to from a single drop the terminal velocity of the new drop will be
- A. \( 2.4 \times 10^{-2} \mathrm{ms}^{-1} \)
- B. \( 15 \times 10^{-2} \mathrm{ms}^{-1} \)
- C. \( 0.75 \times 10^{-2} \mathrm{ms}^{-1} \)
- D. \( 25 \times 10^{-2} \mathrm{ms}^{-1} \)
Step-by-step solution
Volume is conserved: 8 drops of radius a coalesce to form one drop of radius R. Since volume ∝ R^3, R^3 = 8a^3 ⇒ R = 2a. Terminal velocity in a viscous medium (Stokes' law) is v ∝ r^2, so v_new / v_old = (R/a)^2 = 4. Given v_old = 3.75 cm/s = 3.75×10^{-2} m/s, v_new = 4 × 3.75×10^{-2} = 15×10^{-2} m/s.
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