Before You Begin

Question #42346

Difficulty: 8/10 | 🟢 Free

The Question

A solid sphere of mass $m$ and radius $R$ is given an initial angular velocity $\omega_0$ about its horizontal axis and is gently placed on a rough horizontal surface. The initial translational velocity of the center of mass is zero. If the coefficient of kinetic friction between the sphere and the surface is $\mu$ , what is the total work done by the frictional force on the sphere from the moment it is placed on the surface until it begins pure rolling?

Options

A.
$-\frac{1}{7} m R^2 \omega_0^2$
B.
$-\frac{9}{49} m R^2 \omega_0^2$
C.
$\frac{2}{49} m R^2 \omega_0^2$
D.
$-\frac{2}{35} m R^2 \omega_0^2$

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

Work Done by Friction|Impulsive Torque and Angular Momentum|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Work-Energy Theorem and Angular Momentum Conservation during a transition to pure rolling.

A common trap is calculating only the translational work done by friction ( $W_{trans} = \Delta K_{trans} = \frac{2}{49} m R^2 \omega_0^2$ ) or only the rotational work ( $W_{rot} = \Delta K_{rot} = -\frac{9}{49} m R^2 \omega_0^2$ ).

Students must recognize that the total work is the sum of both, which directly equals the total change in kinetic energy, and that this dissipated energy is independent of the friction coefficient $\mu$ .

Quick Facts About This Question

Question Information

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