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Asked in JEE Main 9th April 1st Shift 2019 · Capillary rise
Given: the same liquid and the same contact angle in both tubes, only the radius changing.
The rise is h=(2T cos θ)/(rρ g) and the raised column has mass m=ρπ r²h.
Putting the two together, m=ρπ r²(2T cos θ)/(rρ g)=(2π rT cos θ)/g, so m∝ r.
The same thing read as forces: the meniscus pull 2π rT cos θ carries the whole hanging column, and that pull grows in step with r.
Doubling the radius therefore doubles the mass, giving 2M.
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