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Question #42282

Difficulty: 8/10 | 🟢 Free

The Question

A spherical fluid body of mass $M$ and radius $R$ is initially at rest at a height $h$ in a uniform external gravitational field $g$ . As it falls freely through the distance $h$ , it splits into $8$ identical spherical droplets that move far apart from each other. The fluid is incompressible. Assuming the surface tension energy is negligible compared to the gravitational self-energy, and no energy is dissipated as heat, what is the total kinetic energy of the system of droplets after falling the distance $h$ ?

Options

A.
$Mgh - \frac{9GM^2}{20R}$
B.
$Mgh + \frac{9GM^2}{20R}$
C.
$Mgh - \frac{3GM^2}{5R}$
D.
$Mgh$

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

Gravitational Potential Energy (System)|Bernoulli’s Energy Balance|Potential vs Field Relationship

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to apply the work-energy theorem to an extended, deformable body rather than a simple point mass.

The specific trap is neglecting the change in the internal gravitational self-energy of the fluid body as it changes its structural configuration (splitting into smaller droplets).

Students commonly equate the change in external gravitational potential energy solely to the kinetic energy ( $K = Mgh$ ), ignoring that the separation of the fluid mass requires work against its own self-gravity, which consumes a portion of the available external energy.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Gravitation - Class 11 Part 1
Concept	Gravitational Potential Energy (System)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free