A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. Calculate the initial velocity of the shell

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explos

1.	A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. Calculate the initial velocity of the shell
Answer» Solution :GIVEN Data: m= 200 gm = 0.2 kg , M=4 kg, `"Energy GENERATED" 1.05 KJ =1.05 xx 10^(3) J` According to LAW of Conservation of linear momentum `mv=Mv^(.)` `:. v^(.)=((m)/(M))v` Total K.E of the GUN and bullet `=(1)/(2)Mv^(.2)+(1)/(2)mv^(2)` `=(1)/(2)M((m)/(M)v)^(2)+(1)/(2)mv^(2)` `=(1)/(2)(m^(2)v^(2))/(M)+(1)/(2)mv^(2)` `=(1)/(2)mv^(2)[(m)/(M)+1]` `(1)/(2) xx 0.2 xx v^(2)[1+(0.2)/(4)]=1.05 xx 10^(3)J` `:. v^(2)=(4 xx 1.05 xx 1000)/(0.1 xx 4.2)=100^(2)` `v=100 m // s`