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Question

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 same material) of radius 2r is

A
2M
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B
4M
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C
M/2
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D
M
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Solution

The correct option is A 2M
Mass of water that rises in first capillary =M
Radius of first capillary =r
Radius of second capillary =2r

Let Mass of water that rises in second capillary =M


Applying capillary rise equation:
h=2Tcosθρgr ...(i)

mass M=ρV where (V is volume)
M=ρ×h×A=ρhπr2 ...(ii)

From Eq. (i) & (ii),
M=ρπr2×2Tcosθρgr=2πTrcosθg ...(iii)
Mr
[T and θ will be same as fluid is same]
M(2r)
MM=2rr
M=2M
Hence, 2M amount of mass will rise in capillary tube of radius 2r.

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