## Question

A copper cube of each side 40 cm floats on mercury. the density of copper cube is 3.2g/cc and of mercury is 13.6g/cc at 27° C. the coefficient of volume expansion of Hg and linear expansion of copper are 1.8 * 10^(-4) /°C and 3 * 10^(-6) /°C respectively. Calculate the increase in height i.e. how much block sink further when the temperature rises from 27°C to 100°C?

**Joshi sir comment**

dipped length of the cube in first case = m/Ad here m, A, d are mass of cube, area of the cube and density of mercury respectively

after increasing temperature dipped length in the second case = m/A(1+2αt)[d/(1+γt)]

values are m = VD = 40^{3} 3.2, A = 40^{2}, α = 3 * 10^{-6}, d = 13.6, γ = 1.8 * 10^{-4}, t = 73

all values are in CGS

now solve then substract 1st length from 2nd length