A U-tube is filled with water, and the two arms are capped. ( Figure 1 ) The tub

Question

A U-tube is filled with water, and the two arms are capped.(Figure 1) The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube.

figure 1

A U-tube is filled with water, and the two arms are capped.(Figure 1) The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube. A one-inch depth of sand is poured onto the cap on each arm. (Figure 2) After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap?

Explanation / Answer

Here the height of the sand which is poured is equal and equal to 1 inch.

Let this height is represented by h in meter.

Let the radius of the left arm of the tube = R

Then the radius of the right arm of the tube = 2R

Let the density of the sand = ?
Therefore mass of the sand on the Left hand side = h*?*?*R2 =ML
Mass of the sand on the Right hand side = h*?*?*(2R)2 =4ML
But the pressure at the bottom of the basses of the both left and right arm are same if sand is not present and both will set itself at the same height.This is because the in still liqiuid,pressure is same at the same level.
But here the sand is present and the mass of the sand on the right hand side is more than the mass of the sand on the left hand side.Therefore answer should be the same height

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