Question

If a liquid rises to the same height in two capillaries of the same material at the same temperature, then:

• A. The weight of liquid in both capillaries must be equal
• B. The radius of meniscus must be equal
• C. The capillaries must be cylindrical and vertical
• D. The hydrostatic pressure at the base of capillaries must be same

Answer 1

Answer: (A), (B)

The weight of liquid in both capillaries must be equal
The radius of meniscus must be equal

$h=\frac{2Tcos\theta }{rg\rho }$
$\rho$ ,T,h are same in both capillaries.So
IF $\theta$ is same in both tubes, then their radius of meniscus must be equal(= r).
$⟹$ weight(=$\rho \pi r^{2}hg$)of liquid in both capillaries must be equal.
(C) $⟹$ the above results doesnot require capillary to be cylindrical(only mouth should be circular) or vertical
(D) $⟹$ the hydrostatic pressure at the base of capillaries = P - $\frac{2T}{r}+\rho gh$
where P is pressure exerted by gases trapped above the miniscus
P neednot be same in both tubes $⟹$ hydrostatic pressure at the base of capillaries need not be equal.