As shown in the figuretwo cylindrical vessels A and B are interconnected . Vessel A contains water up to 2m height and vessel B contains kerosene . Liquids are separated by movable, airtight disc C . If height of kerosene is to be maintained at 2m , calculate the mass to be placed on the piston kept in vessel B. Also calulate the force acting on disc C due to this mass. Area of piston =100cm^(2), area of discC=10cm^(2) , Density of water =10^(3)kgm^(-3), specific density of kerosene =0.8.

As shown in the figuretwo cylindrical vessels A and B are interconnect

1.	As shown in the figuretwo cylindrical vessels A and B are interconnected . Vessel A contains water up to 2m height and vessel B contains kerosene . Liquids are separated by movable, airtight disc C . If height of kerosene is to be maintained at 2m , calculate the mass to be placed on the piston kept in vessel B. Also calulate the force acting on disc C due to this mass. Area of piston =100cm^(2), area of discC=10cm^(2) , Density of water =10^(3)kgm^(-3), specific density of kerosene =0.8.
Answer» Solution :Area of piston`A_(1)=100cm^(2)=10^(-2)m^(2)` Area of disc `A_(2)=10cm^(2)=10^(3)m^(2)` Density of water `rho_(w)=10^(3)KGM^(-3)` `therefore` Specific density of kerosene `=("Density of kerosene")/("Density of water")` `=0.8` `therefore` Density of kerosene `rho_(k)` `=0.8xx` density of water `=0.8xx10^(3)` `=800kgm^(-3)` If heightof kerosene is maintained at 2m , Pressure of water column `=(MG)/(A_(1))+` Pressure of kerosene column. `thereforeh rho_(w)g=hrho_(k)g+(mg)/(A_(1))` `therefore2xx10^(3)=2xx800+(m)/(10^(-2))` `therefore2000-1600=(m)/(10^(-2))` `thereforem=400xx10^(-2)` `thereforem=4KG` Now pressure due to mass m is TRANSMITTED undiminished to disc C . So, pressure due to 4kg mass `=("FORCE on disc C")/("Area of disc C")` `therefore(mg)/(A_(1))=(F_(C))/(A_(2))` `thereforeF_(C)=mg((A_(2))/(A_(1)))=4xx9.8xx((10^(-3))/(10^(-2)))` `F_(C)=3.92N`