Question

If a capillary tube of radius 1 mm is immersed in water, the mass of water rising in the capillary tube is m. If the radius of the capillary tube is doubled, then the mass of water that rises in the same capillary tube will be ______.

Options

• 2m

• m

• m/2

• 3m

Answer 1

If a capillary tube of radius 1 mm is immersed in water, the mass of water rising in the capillary tube is m. If the radius of the capillary tube is doubled, then the mass of water that rises in the same capillary tube will be 2m.

Explanation:

Given, r₁ = 1 mm = 1 × 10^-3 m

r₂ = 2r₁ = 2 × 10^-3 m

The height of the water column in a capillary tube is given by,

h = `(2T costheta)/(rhorg)`

⇒ `h ∝ 1/r` ............(i)

Also, the mass of liquid in a column of radius r is given by,

m = (πr²h)ρ

⇒ m ∝ r²h ....................(ii)

From Eqs. (i) and (ii), we get

`m ∝ r^2 xx 1/r` or m ∝ r

∴ `m_1/m_2 = r_1/r_2`

⇒ `m_2 = m(r_2/r_1) = m xx ((2 xx 10^-3)/(1 xx 10^-3))` = 2m