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Question #42363

Difficulty: 8/10 | 🟢 Free

The Question

A long capillary tube of radius $r$ is held vertically such that its lower end just touches the surface of a large pool of liquid of density $\rho$ and surface tension $T$ . The contact angle of the liquid with the tube is zero. The entire setup is placed in an elevator which accelerates upwards with a constant acceleration $a$ . Assuming the liquid flow is non-viscous and neglecting the kinetic energy of the liquid outside the tube, what is the maximum height $H$ reached by the liquid column in the capillary tube relative to the liquid level in the pool?

Options

A.
$\frac{2T}{\rho r (g+a)}$
B.
$\frac{3T}{\rho r (g+a)}$
C.
$\frac{4T}{\rho r (g+a)}$
D.
$\frac{2T}{\rho r g}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Variable Mass Systems|Capillary Rise Mechanics|Vector Analysis

Why This Question Is Tricky

Common Mistakes

This problem tests the dynamics of a variable-mass system in a non-inertial frame.

A common trap is applying the work-energy theorem without accounting for the continuous inelastic collision of the stationary liquid being scooped into the moving column, which dissipates energy and incorrectly yields $H = 4T / \rho r (g+a)$ .

Another trap is assuming static equilibrium $H = 2T / \rho r (g+a)$ .

The correct approach requires applying Newton's second law in the form $dp/dt = F_{net}$ to the variable-mass liquid column, incorporating the pseudo-force due to the elevator's acceleration.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Variable Mass Systems
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free