The lower end of a capillary tube is dipped into water and it is seen that water rises through 7.5 cm in the capillary. Given surface tension of water is `7.5 xx 10^(-2) N//m` and angle of contact between water and glass capillary tube is zero, What will be diameter of the capillary tube ? (Given, `g = 10 ms^(-2)`)

Options

A. 0.2 mm
B. 0.3 mm
C. 0.4 mm
D. 0.5 mm

Answer

C

Explanation

Given, `h = 7.5 cm = 7.5 xx 10^(-2) m , S = 7.5 xx 10^(-2) Nm^(-1)` ,
`theta = 0^(@) , 2 R = ?`
As, ` h = (2S cos theta)/(R rho g)`
`rArr 2R = (4S cos theta)/(h rho g)`
`= (4 xx 7.5 xx 10^(-2) xx cos 0^(@))/(7.5 xx 10^(-2) xx 10^(3) xx 10)`
`= 4 xx 10^(-4) m`
`rArr` Diameter of the capillary tube, `D = 2R = 0.4 mm`