One of the two limbs of a U-tube of uniform bore is closed by means of a cork. Some water and paraffin oil are in the tube. Water level in the open tube is 2 cm higher than that in the closed tube and a 10 cm column of paraffin is above it. If the cork is removed, then by what height will the level of water in the closed limb rise or fall? (Density of paraffin = 0.8g*cm^(-3))

One of the two limbs of a U-tube of uniform bore is closed by means of

1.	One of the two limbs of a U-tube of uniform bore is closed by means of a cork. Some water and paraffin oil are in the tube. Water level in the open tube is 2 cm higher than that in the closed tube and a 10 cm column of paraffin is above it. If the cork is removed, then by what height will the level of water in the closed limb rise or fall? (Density of paraffin = 0.8g*cm^(-3))
Answer» SOLUTION :Let us assume that, when the cork is removed, the water level below the oil column will fall by H with respect to the level of water in the other limb Now, pressure at D = pressure at A. or, `hxx1xxg=10xx0.8xxg` or, h = 8 cm. Here, the cross-section of the U-tube is uniform. So, if the height of the water column FALLS through X cm in ONE limb, the difference in the level of water in the two limbs will increase by 2 x cm. So, the initial difference in the level of water = -2cm and the final difference = +8cm. `therefore" "2x=8-(-2)=10" "thereforex=5cm` So, when the cork is removed, the height of the water column will rise by 5 cm in that limb.