To calculate the energy lost when a ball falls from a height of \(5 \, \text{m}\) and rebounds to a height of \(3 \, \text{m}\): Given: Mass of the ball, \( m = 100 \, \text{g} = 0.1 \, \text{kg} \), Initial height, \( h_1 = 5 \, \text{m} \), Rebound height, \( h_2 = 3 \, \text{m} \), Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \) Calculating the potential energy at height \( h_1 \): \(\text{PE}_1 = mgh_1 = 0.1 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 5 \, \text{m} = 5 \, \text{J}\) Calculating the potential energy at height \( h_2 \): \(\text{PE}_2 = mgh_2 = 0.1 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 3 \, \text{m} = 3 \, \text{J}\) The energy lost is: \(\text{Energy lost} = \text{PE}_1 - \text{PE}_2 = 5 \, \text{J} - 3 \, \text{J} = 2 \, \text{J}\) Thus, the energy lost is: \({2 \, \text{J}}\)