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let x1 be length i in water and x2 in mercury
and x1+x2=h=6 cm...............(1)
here equilibrium equation will be
Weight = total buoyant force for each medium, W=B=Bw + Bhg...........(2)
weight=W= density of cubex volumexg= dc*(A*h)*g, where A is h2
Bw=dw*(A*x1)*g
Bhg=dhg*(A*x2)*g
using equation 2
after cancelling terms on rhs and lhs we get
dc*h=dw*x1+dhg*x2
putting values of density
7.8h=x1+13.6x2..............(3)
solving for x2 using equation 1 and 3
we get , x2 =6.8 h /12.6 =6.8*6/12.6=3.24 cm …......answer for first part
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