A cannon of mass 1000 kg located at the base of an inclined plane fires a shell of mass 50 kg in horizontal direction with velocity 180 km//h. The angle of inclination of the inclined plane with the horizontal is 45^(@). The coefficient of friction between the cannon and inclined plane is 0.5. The maximum height, in metre, to which the cannon can ascend the inclined plane as a result of recoil is

A cannon of mass 1000 kg located at the base of an inclined plane fire

1.	A cannon of mass 1000 kg located at the base of an inclined plane fires a shell of mass 50 kg in horizontal direction with velocity 180 km//h. The angle of inclination of the inclined plane with the horizontal is 45^(@). The coefficient of friction between the cannon and inclined plane is 0.5. The maximum height, in metre, to which the cannon can ascend the inclined plane as a result of recoil is
Answer» `5/6` `5/24` `5/12` NONE of these Solution :Velocity of shell`=180km//h=50m//s` Let `V` be the velocity of the cannon after firing, then form the conservation of linear mometum, `0=50x50-1000VimpliesV=2.5m//s` Let the cannon go up by height h. Net work doen by external forces `=/_\KE` `implies Mgh-"mu"Mgcosthetaxxh/(sintheta)=0-1/2MV^(2)` where `M` is the mass of cannon. SOLVING we GET `h=5/24m`