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The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be

Asked in NEET 2021 · Terminal velocity and its dependences

Answer: (1) (Mg)/2

Step-by-step solution

Given: ball of mass M and density d; glycerine of density σ=d/2; the ball has reached a constant velocity.

Idea: constant velocity means zero acceleration, so weight is balanced by upthrust plus viscous drag.

Volume of the ball: V=M/d

Upthrust: F_B=σ Vg=d/2×M/d× g=(Mg)/2

Balance: Mg=F_B+Fᵥ

Fᵥ=Mg-(Mg)/2=(Mg)/2

Why the other options are wrong

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