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Match List-I with List-II for a small solid sphere of volume V , radius r and density falling through a viscous fluid of density (where > ) and coefficient of viscosity . List-I List-II (A) Buoyant force (I) V g (B) Initial acceleration when just released (II) V( - )g (C) Viscous force at terminal velocity (III) g (1 - ) (D) Terminal velocity (IV) 2r^2( - )g 9 Choose the correct answer from the options given below:

Options

  1. A(A) - (II), (B) - (III), (C) - (I), (D) - (IV)
  2. B(A) - (I), (B) - (II), (C) - (III), (D) - (IV)
  3. C(A) - (II), (B) - (I), (C) - (III), (D) - (IV)
  4. D(A) - (I), (B) - (III), (C) - (II), (D) - (IV)

Correct answer

D. (A) - (I), (B) - (III), (C) - (II), (D) - (IV)

Step-by-step solution

(A) Buoyant force is the weight of the displaced fluid. For a sphere of volume V in a fluid of density , F_b = V g . This matches (I). (B) When just released, the initial velocity is zero, so the viscous force is zero. The net downward force is W - F_b = V g - V g . Initial acceleration a = Net force Mass = V( - )g V = g (1 - ) . This matches (III). (C) At terminal velocity, the sphere moves with constant velocity, so the net force is zero. Viscous force F_v = W - F_b = V g - V g = V( - )g . This matches (II). (D)

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