Sample 1Medium
Eight identical spherical rain drops each fall through air with terminal velocity v. If they coalesce into a single spherical drop, its terminal velocity becomes
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The answer is B.
The volume is conserved, so 8r³ = R³ and R = 2r. Terminal velocity ∝ r² (from Stokes' law), so it becomes 4v.
- A.
2v assumes terminal velocity is proportional to the radius, not its square.
- C.
8v assumes terminal velocity is proportional to the volume.
- D.
16v assumes terminal velocity varies as the fourth power of the radius.
NCERT: Class 11 Physics, Chapter 9, Viscosity (Stokes' law and terminal velocity)