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Question #42312

Difficulty: 8/10 | 🟢 Free

The Question

A sealed horizontal tube of length $L$ is completely filled with an ideal incompressible fluid of density $\rho$ . A small block of volume $V$ and density $\sigma$ (where $\sigma < \rho$ ) is initially at rest at the rear end of the tube. The tube is given a constant horizontal acceleration $a_0$ along its length. Ignoring viscous drag and added mass effects, what is the work done by the fluid on the block in the ground frame from the start of the motion until the block reaches the front end of the tube?

Options

A.
$\frac{\rho^2 V a_0 L}{\rho - \sigma}$
B.
$\frac{\rho \sigma V a_0 L}{\rho - \sigma}$
C.
$\rho V a_0 L$
D.
$(\rho - \sigma) V a_0 L$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Work-Energy Theorem Validity|Frame of Reference|Accelerated Frame Hydrostatics

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Work-Energy Theorem and kinematics across inertial and non-inertial frames in the context of accelerated hydrostatics.

A common trap is calculating the work done by the fluid using the relative displacement in the tube's frame (yielding Option C) or confusing the net work in the non-inertial frame with the work done by the fluid in the ground frame (yielding Option D).

Students must correctly identify that the pressure gradient generates a constant buoyant force, determine the absolute displacement of the block by superimposing the frame's motion with the relative motion, and compute the work in the ground frame.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Work-Energy Theorem Validity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free