Question

An object weights m1 in a liquid of density d1 and that in liquid of density d2 is m2.The density d of the object is

Answer 1

Given:

Density of liquid 1 = d₁

Density of liquid 2 = d₂

Weight of object in liquid 1 = m₁

Weight of object in liquid 2 = m₂

To Find:

The density d of the object.

Calculation:

- Let the volume of object be V.

- Using the concept of buoyancy, we get:

V(d−d₁)g=m₁g

& V(d−d₂)g=m₂g

- Now dividing the above equations we get:

(d − d₁) / (d − d₂) = m₁ / m₂

⇒ m₂ (d − d₁) = m₁ (d − d₂)

⇒ m₂d − m₂d₁ = m₁d − m₁d₂

⇒ d = (m₂d₁−m₁d₂) / (m₂−m₁)

- This is the required density of object.