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A spherical solid ball of volume V is made of a material of density p 1 . It falling through a liquid of density p 1 (p 2 1 ). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., F =-kv 2 (k>0). The terminal speed of the ball is (a) vVg(p 1 -p 2 )/k (b) Vgp 1 /k (c) vVgp 1 /k (d) Vg)p 1 -p 2 /k

 A spherical solid ball of volume V is made of a material of density p1. It falling through a liquid of density p1 (p21). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., F =-kv2(k>0). The terminal speed of the ball is
(a) vVg(p1-p2)/k
(b) Vgp1/k
(c) vVgp1/k
(d) Vg)p1-p2/k

Grade:12th pass

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago

(a) The condition for terminal speed (vt) is

Weight = Buoyant force + Viscous force

? Vp1g = Vp2g + kvt2 ? vt = vVg(p1 – p2 )/k

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