Question

If a capillary of radius $r$ is dipped in water, the height of water that rises in it is h and its mass is M. If the radius of the capillary is doubled the mass of water that rises in the capillary will be :-

• A. $4M$
• B. $2M$
• C. $M$
• D. $\frac{M}{2}$

Answer 1

Answer: (B)

$2M$

In a capillary tube, the height to which a fluid rises is given by,

$H=\frac{2Tcos\theta }{\rho gr}$

Thus, $H\propto R^{-1}$

Hence, for all other parameters constant, on doubling the radius of the tube, the rise in tube will be halved.

Therefore, if M was $\rho \pi R^{2}H$

Hence, new mass will be, $\rho \pi (2R{)}^{2}H/2$

= 2 $\rho \pi R^{2}H$ = 2M