A bullet of mass m and velocity v when fired at a sand bag of mass M , suspended by a string, gets embedded into the bag. The loss of kinetic energy in this process is

Step-by-step solution

Mass of the buIlet =m Speed of bullet =v According to question, bullets gets embedded into the bag, then they will move with common velocity v₁ (say). This is the case of perfectly enelastic collision. Initial kinetic energy of bullet, K_i= 1 2 m v^2 By the conservation of linear momentum, aligned m v & =(M+m) v₁ & v₁= m v M+m aligned Final kinetic energy, K_f= 1 2 (M+m) v₁^2 aligned & = 1 2 (M+m) m^2 v^2 (M+m)^2 [from Eq. (ii)] & = 1 2 m^2 v^2 M+m aligned Loss in kine tic energy =K_i-K_f aligned & = 1 2 m v^2- 1 2