A piece of metal floats in mercury. The coefficients of volume expansion of the metal and mercury are γ 1 and γ 2 , respectively. If the temperatures of both mercury and the metal are increased by Δ T , the fraction of the volume of the metal submerged in mercury changes by the factor of

Step-by-step solution

As, γ 1 = Δ V 1 V 1 Δ T and γ 2 = Δ V 2 V 2 Δ T ⇒ Δ V 1 = γ 1 V 1 Δ T and Δ V 2 = γ 2 V 2 Δ T Fraction of volume submerged before temperature is raised is given by f ⁡ = ρ 1 / ρ 2 . Fraction of volume submerged after the temperature is raised is given by f ⁡ ′ = ρ 1 ′ / ρ 2 ′ . α ′ = ρ 1 1 + γ 1 Δ T 1 + γ 2 Δ T ρ 2 = ρ 1 ρ 2 1 + γ 2 Δ T 1 + &g