Energy Conservation

The potential energy lost in the fall is proportional to the height fallen. Given that 50\% of the energy is lost after the ball hits the ground, the remaining energy determines the maximum height reached, which is 5 m. Thus, the correct answer is option (3).

Step 1: Use energy conservation principle For a solid cylinder rolling down an inclined plane, the total energy is conserved. The potential energy at the top of the incline is converted into kinetic energy at the bottom. The potential energy at height is: At the bottom, the kinetic energy of the cylinder is a combination of translational and rotational energy. The total kinetic energy is: For a solid cylinder, the moment of inertia is given by and the relation between linear velocity and angular velocity is . Substituting this into the expression for kinetic energy: Step 2: Equating potential and kinetic energy From conservation of energy: Solving for : Thus, the speed of the cylinder at the bottom is: