A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be

Options

A. 4 cm
B. 20 cm
C. 8 cm
D. 10 cm

Answer

B

Explanation

Consider the situation wherea capillary tube is dipped in water of density p. Net force on the liquid due to surface tension will be upwards and is balanced by the downward force of the weight
`w=pir^(2)h pg="weight of liquid"`
`"So", 2pirS cos theta` =Net force due to surface tension
`Rightarrow pir^(2)hpg=2pirS cos theta`
Where, S is surface tension and `theta` is the constant angle.
`Rightarrow h(2S cos theta)/(rpg)Rightarrow h alpha (1)/(g)`
Where, g is acceleration due to gravity
When the entire arrangement is falling with an acceleration g.
`g_("eff")=g-g=0`
`"Hence", h' alpha (1)/(g_("eff"))=(1)/(0)=oo`
Hence there is a overflow in the capillary tube. As length of the capillaryly tube is l.
`Rightarrow h'=l=20cm`