The linear expansivity of a metal P is twice that of another metal Q. When these materials are heated through the same temperature change, their increase in...

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Let the original length of metal P be x and the original length of metal Q be y. We know that the increase in length is given by: ΔL = L₀αΔθ where ΔL is the increase in length, L₀ is the original length, α is the coefficient of linear expansion, and Δθ is the change in temperature. Since the increase in length is the same for both metals, we can write: ΔL_P = ΔL_Q L_Pα_PΔθ = L_Qα_QΔθ L_P/L_Q = α_Q/α_P Since we are told that the linear expansivity of P is twice that of Q, we can write: α_P = 2α_Q Substituting into the equation above, we get: L_P/L_Q = α_Q/2α_Q = 1/2 Therefore, the ratio of the original length of P to that of Q is 1:2. Answer: 1:2