A metal sphere of volume V has a terminal velocity 2m/s in glycerine. The terminal velocity of sphere of volume 8V in glycerine will be-:

Question

a)4m/s

b)8m/s

c)16m/s

d)32m/s

Answer 1

Apply the concept formula to get the answer

When a sphere of radius r moves with a velocity v through a fluid of viscosity η, the viscous force opposing the motion of the sphere is

F = 6πη r v

If for a sphere viscous force become equal to the net weight acting downward, the velocity of the body become constant and is known as terminal velocity.

6πη r vT = (4/3) πr3 (ρ – σ)g

Comments

This formula leads me to v=k.r^2=k.V/r
which gives me v=k.V
and it give me v=16m/s which is wrong, the answer is 8m/s ?