MHT CET · Physics · Mechanical Properties of Fluids

In a capillary tube of radius $R$ , a straight thin metal wire of radius $r$ $(R > r)$ is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is [ $T =$ surface tension of water, $ρ$ = density of water, $g =$ gravitational acceleration]

A $\frac{T}{(R + r) ρ g}$
B $\frac{2T}{(R + r) ρ g}$
C $\frac{2 T}{(R - r) ρ g}$
D $\frac{(R - r) ρ g}{T}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{2 T}{(R - r) ρ g}$

Step-by-step Solution

Detailed explanation

h = \frac{2 T c o s θ}{ρ g (R - r)}

For

\cos θ = 0,

h = \frac{2 T}{ρ g (R - r)}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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