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Question

A capillary tube of length 5TRρg and cross-section radius R contain fluid column of length l where l=3TRρg. This capillary tube is kept vertical. Surface tension and density of fluid are T and ρ respectively. Contact angle between fluid and the material of tube can be zero.

A
Shape of meniscus is concave towards air at both top at bottom
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B
Shape of meniscus is concave towards air at top and convex towards air at bottom
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C
Radius of curvature of fluid at top is R
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D
Radius of curvature of fluid at bottom is 2R
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Solution

The correct options are
B Shape of meniscus is concave towards air at top and convex towards air at bottom
C Radius of curvature of fluid at top is R
D Radius of curvature of fluid at bottom is 2R
Meniscus at the top has no constaints, so it will behave like normal and hence its shape will be concave towards air. As we go from point 1 to point 2 inside the liquid, pressure increases. If this increment in pressure is greater than 2TR, then the meniscus will become convex.
So increment in pressure ρgh = (ρg(3TRρg) = 3TR> 2TR, Hence meniscus will be convex towards air at bottom.

Since contact angle between fluid and material is zero, hence radius of curvature of fluid at top will be R.

For meniscus at bottom,
P1 = P0 2TRP2 = P0 2TR + ρgl= P0 2TR + ρg(3TRρg)= P0 + TR= P0 + 2T2R
Comparing with
P0 + 2TReq , we get Req = 2R

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