Question

Two solid spheres of same metal but of mass M and 8M full simultaneously on a viscous liquid and their terminal velocity are V and 'nV' then value of 'n' is 

(A) 16 

(B) 8 

(C) 4 

(D) 2

Answer 1

Correct option: (C) 4

Explanation:

Mass = density × volume

As material is same, density is same hence

mass ∝ volume

∴ M ∝ (4/3) πr³ i.e. M ∝ r³ 

∴ (M₁ / M₂) = (r₁ / r₂)³ i.e (M / 8M) = (r₁ / r₂)³ i.e (r₁ / r₂) = (1/2)

Hence

r₂ = 2r₁         (1)

Also terminal Velocity = V = (2/g) (r²g / η(ρ – σ)

As all factors except r are constant

V ∝ r² 

∴ (V₂ / V₁) = (r₂ / r₁)² 

(V₂ / V₁) = (2r₂ / r₁)² ------ from (1)

(V₂ / V₁) = 4

Hence

V₂ = 4V₁ 

Given is V₁ = V & V₂ = n ∙ V

Hence [{n ∙ V} / V] = 4 i.e. n = 4