Question

A spherical solid ball of volume V is made of a material of density p₁.It is falling through a liquid of density p₂(p₂ < p₁ ). [Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e.,F_viscous = -Kv²(k > 0)]. The terminal speed of the ball is

(a) √{Vg(p₁ - p₂)/k}

(b) Vgp₁/k

_(c) √(Vgp₁/k)

(d) Vg(P_{1 -} p₂)/k

Answer 1

Correct Option (a) √{Vg(p₁ - p₂)/k}

Explanation:

The forces acting on the ball are gravity force, buoyancy force and viscous force. When ball acquires terminal speed, it is in, dynamic equilibrium, let terminal speed of ball be v_T. So,