JEE Advanced · Physics · 11. Properties of Fluids

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius $0.1 mm$ is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume $V_{0}$ to $\frac{100}{101} V_{0}$ with the movable piston.Considering air as an ideal gas, the height $(h)$ of the liquid column in the capillary above the liquid level in $cm$ is _____.
[Given: Surface tension of the liquid is $0.075 N m^{- 1}$ , atmospheric pressure is $10^{5} N m^{- 2}$ , acceleration due to gravity $(g)$ is $10 m s^{- 2}$ , density of the liquid is $10^{3} kg m^{- 3}$ and contact angle of capillary surface with the liquid is zero]

A 21
B 23
C 25
D 27

Verified Solution

Answer & Solution

Correct Answer

(C) 25

Step-by-step Solution

Detailed explanation

Let

P_{f}

be the air pressure. As the process is isothermal, we can write

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.

Same subject

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From JEE Advanced

Columns 1, 2 and 3 contain starting materials, reaction conditions and type of reactions respectively.

Column 1	Column 2	Column 3
(I) Toulene	(i) $NaOH$ $ /Br _2$	(P) Condensation
(II) Acetophenone	(ii) $B r_2 / h v$	(Q) Carboxylation
(III) Benzaldehyde	(iii) $\left( CH _3 CO \right)_2$ $O / CH _3$ $COOK$	(R) Substitution
(IV) Phenol	(iv) $NaOH$ $/CO _2$	(S) Haloform

The only CORRECT combination in which the reaction proceeds through radical mechanism is

JEE Advanced 2017 Medium

let

f_{1} : R \to R, f_{2} : [0, \infty) \to R, f_{3} : R \to R a n d f_{4} : R \to [0, \infty)

be defined by

f_{1} (x) = \{\begin{matrix} |x| & i f & x < 0 \\ e^{x} & i f & x \geq 0 \end{matrix}; f_{2} (x) = x^{2}; f_{3} (x) = \{\begin{matrix} \sin x & i f & x < 0 \\ x & i f & x \geq 0 \end{matrix} a n d f_{4} (x) = \{\begin{matrix} f_{2} (f_{1} (x)) & i f & x < 0 \\ f_{2} (f_{1} (x)) - 1 & i f & x \geq 0 \end{matrix}

	List – I		List – II
(A)	$f_{4}$ is	(P)	Onto but not one – one
(B)	$f_{3}$ is	(Q)	neither continuous nor one-one
(C)	$f_{2}$ of $f_{1}$ is	(R)	differentiable but not one-one
(D)	$f_{2}$ is	(S)	continuous and one-one

JEE Advanced 2014 Medium

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