Question

The fraction of floating object of volume V₀ and density d₀ above the surface of a Liquid as density d will be 

(A) (d₀ / d) 

(B) [{dd₀} / {d + d₀}] 

(C) [{d – d₀} / d] 

(D) [{dd₀} / {d – d₀}]

Answer 1

Correct option: (C) [{d – d₀} / d]

Explanation:

When object floats, according to Newton’s third law, buoyant force of liquid has an opposite direction and same magnitude as the weight force of the floating object.

From this condition, we obtain equation of force equilibrium.

d ∙ g ∙ V_in = mg ----- where V_in – volume of object which is immersed in the liquid.

Also m = dV = mass of the object

Hence

d ∙ g ∙ V_in = d₀ ∙ V ∙ g

∴ d V_in = d­₀ V

(V_in / V) = (d₀ / d)

∴ 1 – (V_in / V) = 1 – (d₀ / d)

[{V – V_in­} / V] = [{d – d₀} / d]

Here V – V_in = volume of floating object

∴ [{V_floating} / V] = [{d – d₀} / d]