Question

In a capillary tube of radius R, a straight thin metal wire of radius r (R > r) is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is ______.

[T = surface tension of water, ρ = density of water and g = gravitational acceleration]

Options

• `"T"/(("R"+"r")(rho"g"))`

• `("R"rho"g")/(2"T")`

• `(2"T")/(("R"-"r")(rho"g"))`

• `(("R"-"r")(rho"g"))/"T"`

Answer 1

In a capillary tube of radius R, a straight thin metal wire of radius r (R > r) is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is `underlinebb((2"T")/(("R"-"r")(rho"g")))`.

Explanation:

Rise of water in the capillary tube (h) is given by

h = `(2"T"costheta)/(rho"g"("R"-"r"))`

In the given case,

cosθ = 1 as θ = 0°

∴ h = `(2"T")/(("R"-"r")(rho"g"))`