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**Hint**We know that the pressure at a point $A$ and $B$ in the diagram is the same. The pressure drop when going downwards through the meniscus from the point $A$ is $\dfrac{{2T}}{R}$, where $T$ is the surface tension of water and $R$ is the radius of the meniscus. This pressure drop is compensated by the pressure of the water column. Once we balance these, we will get our required solution.

**Complete Step by step solution**The height of the water column is calculated from the equation $\rho gh = \dfrac{{2T}}{R}$, where $\rho $ is the density of water, $h$ is the height of the water column, $g$ is the acceleration due to gravity, $T$ is the surface tension of water, and $R$ is the radius of the meniscus. Now from the figure, we get $\cos \theta = \dfrac{R}{r}$, i.e. $R = r\cos \theta $ such that the above equation becomes $\rho gh = \dfrac{{2T}}{{r\cos \theta }}$.

Also, we need to find the mass of the water column in terms of the height and radius of the cylinder. If $M$ be the mass of the water column, then $M = \rho V = \rho (\pi {r^2}h)$. Substituting $h$ from the above equation, we get $h = \dfrac{M}{{\rho \pi {r^2}}}$.

Replacing $h$, in the equation $\rho gh = \dfrac{{2T}}{{r\cos \theta }}$, we get $\dfrac{{\rho gM}}{{\rho \pi {r^2}}} = \dfrac{{2T}}{{r\cos \theta }}$.

Cancelling terms and taking all constants on one side we get, $\dfrac{M}{r} = \dfrac{{2\pi T}}{{g\cos \theta }} = const.$

Now according to the given question, the mass of water in the capillary tube is $5grams$, and the radius $r$ gets doubled.

$ \Rightarrow \dfrac{M}{r} = const. = \dfrac{{{M_1}}}{{{r_1}}} = \dfrac{{{M_2}}}{{{r_2}}}$,

$ \therefore \dfrac{{5grams}}{{{r_1}}} = \dfrac{{{M_2}}}{{2{r_1}}}$, or ${M_2} = 10grams$.

**Therefore the correct option is an option (B).**

**Note**Here we take the pressure drop as $\dfrac{{2T}}{R}$ and not $\dfrac{{4T}}{R}$, since the water column has only a single layer. In the case of bubbles, the pressure difference between the concave and the convex sides is $\dfrac{{4T}}{R}$. The concave side of a bubble has more pressure than the concave side.

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