A metal piece of density 8g*m^(-3) is suspended from a wooden hook by an weightless string. The tension in the string is 56g times g. What will be the tension in the string, if the system is immersed in a liquid at 40^(@)C? The surrounding temperature during the experiment is 20^(@)C. At 20^(@)C the specific gravity of the liquid is 1.24. The coefficients of volume expansion of the liquid and the metal are 4 times 10^(-5@)C^(-1) " and " 8 times 10^(-4@)C^(-1) respectively.

A metal piece of density 8g*m^(-3) is suspended from a wooden hook by

1.	A metal piece of density 8g*m^(-3) is suspended from a wooden hook by an weightless string. The tension in the string is 56g times g. What will be the tension in the string, if the system is immersed in a liquid at 40^(@)C? The surrounding temperature during the experiment is 20^(@)C. At 20^(@)C the specific gravity of the liquid is 1.24. The coefficients of volume expansion of the liquid and the metal are 4 times 10^(-5@)C^(-1) " and " 8 times 10^(-4@)C^(-1) respectively.
Answer» Solution :Volume of the metal piece at `20^(@)C`, `V_(20)=56/8=7cm^(3)` `therefore` Volume at `40^(@)C,` `V_(40)=V_(20)[1+8 times 10^(-4) times 20]` `""=7(1+8 times 10^(-4) times 20)cm^(3)` Volume of the displaced liquid `=V_(40)` `therefore` Mass of displaced liquid `=V_(40) times rho_(40)` `""[rho_(40)=` density of the liquid at `40^(@)C]` i.e., weight of the displaced liquid `=V_(40) times rho_(40) times g` `therefore` upthrust `""=V_(40) times rho_(40) times g` `""=7[1+8 times 10^(-4) times 20] times 1.24/(1+20 times 4 times 10^(-5)) times 980` `""=7 times 1.24[1+0.016][1+8 times 10^(-4)]^(-1) times 980` `""=7 times 1.24 times 1.016[1-0.0008] times 980` `""=7 times 1.24 times 1.016 times 0.9992 times 980=8.81 times 980 dyn.` `therefore` Tension in the string `"" =(56-8.81) times 980=4.625 times 10^(4)dyn.`