Question

A capillary tube of radius r is immersed in water and water rises in it to a height of h. The mass of water in the capillary tube is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is ______

Options

• 2.5 g

• 5.0 g

• 10 g

• 20 g

Answer 1

A capillary tube of radius r is immersed in water and water rises in it to a height of h. The mass of water in the capillary tube is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is 10 g.

Explanation:

Height of liquid in liquid column is,

h = `(2Tcostheta)/(rrhog)`

∴ Mass of liquid in column = `pir^2hrho` (∵ Mass= volume x density)

∴ m = `pir^2((2Tcostheta)/(rrhog))rho`

∴ m = `((2piTcostheta)/g)r`

∴ m ∝ r  or `m_1/m_2 = r_1/r_2`

or `5/m_2 = r/(2r)` or m₂ = 10 g