A stationary object at 4^ C and weighing 3.5 kg falls from a height of 2000 m on snow mountain at 0^ C . If the temperature of the object just before hitting the snow is 0^ C and the object comes to rest immediately then the quantity of ice that melts is (Acceleration due to gravity =10 ~m / s ^2 , Latent heat of ice .=3.5 10^5 ~J / kg )

Step-by-step solution

The object's gravitational potential energy at height h is converted entirely into heat upon impact. Using g = 10 m s⁻² , the energy released is mgh = (3.5)(10)(2000) = 70,000 J . This heat melts a mass m of ice at 0^ C , satisfying mL_f = 70,000 , where L_f = 3.5 10^5 J kg⁻¹ . Solving gives m = 70,000 3.5 10^5 = 2 10 = 0.2 kg . The mass melted is 0.2 1000 = 200 g . The quantity of ice melted is 200 g .