Physics - Fluid Question with Solution | TestHub

The height of capillary rise is given by $H=\frac{2T\cos \theta }{\rho gR}$

The mass of water in the capillary tube is $M=\pi R^{2}H\rho$

Substituting the expression for $H$, we get:

$M=\pi R^2\left(\frac{2T\cos \theta }{\rho gR}\right)\rho =\frac{2\pi RT\cos \theta }{g}$

This shows that the mass of water in the capillary tube is directly proportional to its radius, i.e., $M\propto R$.

For the second capillary tube, the radius is doubled ($R^{\prime }=2R$).

Therefore, the new mass of water will be $M^{\prime }=2M$.

Answer: $2M$