The cross-sections of the two sides of a U-tube are 1cm^(2)and0.1cm^(2) respectively. Some water is poured inside the tube when it rise to the same height in both the limbs. What volume of a liquid of density 0.85g*cm^(-3) should be poured into the wider limb so that the water level rises by 15 cm in the narrow limb?

The cross-sections of the two sides of a U-tube are 1cm^(2)and0.1cm^(2

1.	The cross-sections of the two sides of a U-tube are 1cm^(2)and0.1cm^(2) respectively. Some water is poured inside the tube when it rise to the same height in both the limbs. What volume of a liquid of density 0.85g*cm^(-3) should be poured into the wider limb so that the water level rises by 15 cm in the narrow limb?
Answer» Solution :At first, water rises up to the same level in both the arms. When the liquid is POURED into the wider limb, suppose the level of water FALLS by x cm and rises by 15 cm in the narrow limb. AC = BF = x , volume of the part AC = volume of the part BD or, `x xx1=15xx0.1or,x=1.5cm` Let EC = h. Pressure at the point C = pressure at the point F or, `hxx0.85xxg=(15+1.5)xx1xxg` or, `h=16.5/0.85=19.41`cm So, the volume of liquid poured into the wider limb = `19.41xx1=19.41cm^(3)`.