Question

Water rises in a capillary tube of radius r upto a height h. The mass of water in a capillary is m. The mass of water that will rise in a capillary of radius `"r"/4` will be ______.

विकल्प

• 4m

• `"m"/4`

• m

• `4/"m"`

Answer 1

Water rises in a capillary tube of radius r upto a height h. The mass of water in a capillary is m. The mass of water that will rise in a capillary of radius `"r"/4` will be `"m"/4`.

Explanation:

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

`"h"=(2"T"costheta)/(rho "rg")`

⇒ `"h"prop1/"r"`  ...(i)

Also, mass of liquid in a column of radius r and height h, is

`"m" = (pi"r"^2"h")rho`

⇒ `"m" prop "r"^2"h"`  ...(ii)

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

`"m" prop "r"^2xx1/"r"`

`"m" prop "r"`

⇒ `"m"^'/"m"=("r"/4)/"r"` ⇒ `"m"^'="m"/4`