When a block of iron floats in mercury at 0 degrees C, a fraction K1 of its volume is submerged while at the temperature of 60 degrees, a fraction K2 is seen to be submerged. If the coefficient of volume expansion of iron is ∂Fe and that of mercury is ∂Hg, then the ratio K1/K2 is?
I got one answer as K1/K2 = 1+60∂Fe/1+60∂Hg
There is one more answer given as K1/K2 = 1-60∂Hg/1-60∂Fe
How do we get that?
23Vimmersed ÏHgg = Vtotal ÏFe g
so Vimmersed Vtotal = ÏFeÏHg
now Ï = mV = mVo(1+γΔτ) = Ïo(1+γΔτ)
i.e Ï= Ïo(1+γΔτ) ≈ Ïo (1 - γΔτ) [ by binomail approximation
now the 2nd answer is given by directly using the equation for density as a function of T USING binomial approximation , while the first ans is exact . but therez not much difference
