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Question #42313

Difficulty: 8/10 | 🟢 Free

The Question

A solid sphere of mass $m$ and radius $R$ translates with a velocity $v_0$ without rotation on a smooth horizontal plane. It suddenly encounters a perfectly rough horizontal plane, causing it to instantaneously achieve pure rolling. What is the magnitude of the work done by the impulsive friction force during this instantaneous transition?

Options

A.
$\frac{1}{7} m v_0^2$
B.
$\frac{2}{7} m v_0^2$
C.
$\frac{5}{14} m v_0^2$
D.
$0$

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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

Work-Energy Theorem Validity|Conservative vs Non-conservative|Pure Rolling Condition

Why This Question Is Tricky

Common Mistakes

This question tests the misconception that friction does no work when a body enters a pure rolling state.

While static friction does zero work during pure rolling, the impulsive friction required to instantaneously transition the sphere from sliding to rolling is kinetic in nature and dissipates energy.

Students often erroneously apply the conservation of mechanical energy (yielding zero work) or fail to recognize that angular momentum must be conserved about the point of contact to bypass the complex integration of the impulsive non-conservative force.

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