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A tank contains water on top of mercury.A cube of iron,60mm along each edge,is sitting upright in equilibrium in the liquids.Find how much of it is in each liquid.The densities of iron and mercury are 7.7g/cm 3 and 13.6g/cm 3 respectively

A tank contains water on top of mercury.A cube of iron,60mm along each edge,is sitting upright in equilibrium in the liquids.Find how much of it is in each liquid.The densities of iron and mercury are 7.7g/cm3 and 13.6g/cm3 respectively

Grade:12

1 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
11 years ago

Dear Sohan

Suppose x1 length is in water and x2 in mercury

and x1+x2=h=60mm...............(1)

here equilibrium equation will be

Weight = total buoyant force for each medium,  W=B=Bw + Bhg...........(2)

weight=W= density of cubex volumexg= dcx(Axh)xg,   where A is h2

Bw=dw*(A*x1)*g

Bhg=dhg*(A*x2)*g

use equation 2

after cancelling terms on rhs and lhs you will get

dc*h=dw*x1+dhg*x2

put values of density

7.7h=x1+13.6x2..............(3)

solve for x1 and x2 using 1 and 3

x2=6.7h/12.6= 6.7*60/12.6 = 31.9 mm in mercury

in water=60-31.9=28.1 mm

 All the best.                                                          

AKASH GOYAL

AskiitiansExpert-IIT Delhi

 

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