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Question #42479

Difficulty: 8/10 | 🟢 Free

The Question

A uniform cubical block of mass $m$ and side length $a$ rests on a horizontal surface. A constant horizontal force $F = \frac{1}{2}mg$ is applied at the top edge of the block, directed to the right. The surface has a variable coefficient of kinetic friction $\mu = cx$ , where $x$ is the displacement of the block from its initial position and $c$ is a positive constant. The block starts from rest at $x=0$ and slides without rotating. At a critical displacement $x_0$ , the block begins to topple about its leading bottom edge. Assuming the leading edge does not slip once toppling begins, what is the kinetic energy of the block \textit{just after} the transition to pure rotation?

Options

A.
$\frac{3mg}{64c}$
B.
$\frac{mg}{8c}$
C.
$\frac{3mg}{32c}$
D.
$\frac{mg}{16c}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Work-Energy Theorem Validity|Toppling vs Sliding|System of Particles and Rotational Motion

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous mechanics of the transition from pure translation to pure rotation (toppling).

The primary trap is assuming that kinetic energy is conserved during the onset of toppling.

Students often correctly calculate the kinetic energy just before toppling using the Work-Energy theorem, but fail to recognize that the sudden shift of the pivot to the leading edge introduces an impulsive normal and frictional force.

This requires applying conservation of angular momentum about the new pivot, which reveals a fundamental partitioning and loss of energy during the transition.

Additionally, it tests the constraint equation N(x)=0 at the trailing edge to find the critical toppling displacement, catching those who ignore the torque contribution of the friction force itself.

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