A rubber ball is dropped from a height of 5 ~m on a planet, where the acceleration due to gravity is not known. On bouncing it rises to 1.8 ~m . The ball loses its velocity on bouncing by a factor of

Step-by-step solution

Key Idea According to conservation of energy, potential energy at height h= kinetic energy at ground. Potential energy = Kinetic energy ie, m g h= 1 2 m v² v= 2 g h If h₁ and h₂ are initial and final heights, then v₁= 2 g h₁ , v₂= 2 g h₂ Loss in velocity v=v₁-v₂= 2 g h₁ - 2 g h₂ Fractional loss in velocity = v v₁ array l = 2 g h₁ - 2 g h₂ 2 g h₁ =1- h₂ h₁ array Substituting the values, we have v v₁ =1- 1.8 5 array l =1- 0.36 =1-0.6 =0.4= 2 5 array