A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to a 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m i $s ______$ J.
(g = 10 m/s²)

Question

A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to a 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m i $s ______$ J.

(g = 10 m/s²)

G1 Physics · Accepted Answer

Treat the flywheel as a solid disc, as done in the supplied source. Its moment of inertia is I = ½MR². Here, M = 3 kg, R = 5 m. The hanging mass is also m = 3 kg. When the mass descends by h = 3 m, the loss in gravitational potential energy is mgh = 3×10×3 = 90 J. Let the speed of the falling mass be v. Since the string does not slip, v = ωR. Translational kinetic energy of the hanging mass is K(trans) = ½mv². Rotational kinetic energy of the flywheel is K(rot) = ½Iω² = ½(½MR²)(v²/R²). Since M…