Question

The velocity of a small ball of mass m and density d₁ when dropped in a container filled with glycerine becomes constants after sometime. What is the viscous force acting on the ball ? (density of glycerine is d₂)

(A) mg{1 – (d₁ / d₂)}

(B) mg{1 – (d₂ / d₁)}

(C) mg{d₁ / (d₁ – d₂)}

(D) mg{d₂ / (d₁ – d₂)}

Answer 1

The correct option is (B) mg{1 – (d₂ / d₁)}.

Explanation:

viscous force = weight – buoyant force 

= Vd₁ g – Vd₂ g 

= Vd₁ g {1 – (d₂ / d₁)} 

But mass = m = d₁ V 

Hence viscous force = mg{1 – (d₂ / d₁)}