If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is:

We begin with the well-known expression for the height to which a liquid of density $$\rho$$ rises in a capillary tube of radius $$r$$ due to surface tension. The formula is stated as

$$h=\frac{2T\cos\theta}{\rho g\,r},$$

where $$T$$ is the surface-tension coefficient of the liquid, $$\theta$$ is the angle of contact, and $$g$$ is the acceleration due to gravity.

Now, the volume of the liquid column inside the tube is obtained from the usual cylinder relation

$$V=\pi r^{2}h.$$

To convert this volume into mass, we multiply by the density $$\rho$$ because mass and volume are connected through the formula $$m=\rho V$$. Substituting the above volume, we have

$$m=\rho\bigl(\pi r^{2}h\bigr).$$

At this stage we substitute the value of $$h$$ from Jurin’s law. Thus

$$m=\rho\bigl(\pi r^{2}\bigr)\left(\frac{2T\cos\theta}{\rho g\,r}\right).$$

Notice that the factor $$\rho$$ appears in both the numerator and the denominator, so it cancels out completely. Carrying out this cancellation and also cancelling one factor of $$r$$ between the numerator and denominator, we obtain

$$m=\frac{2\pi T\cos\theta}{g}\,r.$$

This final algebraic form shows clearly that the mass $$m$$ of the liquid column is directly proportional to the radius $$r$$ of the capillary tube. In simpler words, we can write

$$m\propto r.$$

We are told that when the radius is $$r$$, the mass of the water column is $$M$$. Symbolically,

$$M=k\,r,$$

where $$k=\dfrac{2\pi T\cos\theta}{g}$$ is the proportionality constant comprising only fixed physical quantities.

Next, we increase the radius to $$2r$$. According to the direct proportionality, the new mass $$M'$$ must satisfy

$$M'=k\,(2r)=2\,k\,r.$$

But $$k\,r$$ is nothing but our original mass $$M$$. Therefore, substituting, we find

$$M'=2M.$$

So doubling the radius doubles the mass of water that rises in the capillary.

Hence, the correct answer is Option B.