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The cross-section of the two limbs of a ...

The cross-section of the two limbs of a U-tube are `3cm^(2)and1cm^(2)` respectively. Keeping the tube vertical, some mercury is poured into it. Now `60cm^(3)` of water is poured into the wider limb. To what height will the mercury rise in the narrow limb? The density of mercury = `13.6g*cm^(-3)`.

Text Solution

Verified by Experts

We can see the final state after water is poured. The mercury column in the wider limb will fall and that in the narrow limb will rise.

The height of the water column in the wider limb
`=("volume of water")/("area of cross-section of the wider limb")=60/3=20cm`
`therefore" "`FC = 20 cm
After water is poured into the wider limb, suppose the mercury column falls by x. So, mercury will rise through 3x in the narrower limb (`because` the area of the cross-section of the wider limb is 3 times that of the narrower limb).
`therefore" "`AC = x and BE = 3x
`therefore" "`DE = x + 3x = 4x
Now, pressure at the point C = pressure at the point D
or, `20xx1xxg=4x xx13.6xxg`
or, `x=20/(4xx13.6)=0.368`cm
`therefore" "` The mercury column will rise through `0.368xx3` = 1.1 cm in the narrower limb.
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