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A shell of mass 200 gm is ejected from a...

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

Text Solution

Verified by Experts

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`
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