A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 m s⁻¹. The absolute value of work done on the disc to stop it i s ______ J.
Physics · Rotational Motion · Combined Translational & Rotational Motion
JEE Mains 2024 31 Jan Morning Shift

Question

A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 m s⁻¹. The absolute value of work done on the disc to stop it i s ______ J.

G1 Physics · Accepted Answer

For rolling without slipping: K = (1/2)mv² + (1/2)Iω² For a solid disc: I = (1/2)mR², ω = v/R K = (1/2)mv² + (1/4)mv² = ( 3 4 \frac{3}{4} 4 3 ​ )mv² = ( 3 4 \frac{3}{4} 4 3 ​ )(50)(0.4)² = 6 J The work done to stop the disc is -6 J, so its absolute value is 6 J.