JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Fluid Mechanics

If ' M ' is the mass of water that rises in a capillary tube of radius '

r

', then mass of water which will rise in a capillary tube of radius '

2 r

' is:

(A)4 M
(B) $\frac{M}{2}$
(C)M
(D)2 M✓ Correct

Answer: (D)

Solution

The capillary rise is

h = \frac{2 T c o s θ}{ρ r g}

, so

h \propto \frac{1}{r}

and doubling the radius halves the height. The mass held is

M = π r^{2} h ρ

; for radius

2 r

this becomes

π (2 r)^{2} (\frac{h}{2}) ρ = 2 π r^{2} h ρ = 2 M

, so twice the mass rises.

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option

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