Question

A cubical metal block of edge 12 cm floats in mercry with one fifth of the height inside the mercury. Water poured till the surface of the block is just immersed in it. Find the height of the block is just immersed in it. Find the height of the water column to be poured. Specific gravity of mercury =13.6.

Answer 1

`a` : edge of cube
Case I `W = F_B = rho_m V_(i n) g`
=`rho_m a^2 .(a)/(5) g`…(i)
Case II `W = rho_m V_m g+ rho_omega V_omega g`
`rho_m a^2.(a)/(5)g = rho_m a^2 h g+ rho_omega a^2(a - h)g`
`h` : length immersed in mercury
`(rho_m a)/(5) = rho_m h + rho_m (a - h) = (rho_m - rho_omega)h + rho_omega a`
`h = (((rho_m)/(5) - rho_omega)a)/((rho_m - rho_omega))`
=`(((13.6)/(5) -1)xx 12)/((13.6 -1)) = 1.64 cm`
`a - h = 12 - 1.64 = 10.36 cm`.
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