Eight drops of water, each radius 2mm are falling through air at a terminal velocity of 8cms-1. If they coalesce to form a single drop the terminal velocity of the combined drop will be:
Correct answer: D. 32 cms-1
- A. 8 cms-1
- B. 16 cms-1
- C. 24 cms-1
- D. 32 cms-1
Explanation
Explanation is given below.Let the radius of bigger drop is R and smaller drop is r then4/3πR^3 = 8×4/3×πr^3or R=2r ....(i)Terminal velocity,vt = 2 r^2(ρ−σ)g/9η vt ∝ r^2 v'/v = R^2 / r^2 =(2r/r)^2 =4 (Using (i))or v′ =4v=4×8=32cms^−1As it is numerical, it can have only one possible answer.
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About Terminal Velocity
Terminal velocity is the constant speed reached when gravitational force is balanced by fluid resistance. The topic covers drag, buoyant force, the conditions for zero acceleration, and how viscosity, object size, shape and density affect the limiting speed, with a distinction between free fall before and after terminal velocity.
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