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Asked in NEET 2008 · Recoil and explosions
Given: shell m=0.2 kg, gun M=4 kg, total energy released E=1050 J.
Idea: the pair starts at rest, so the gun recoils with equal and opposite momentum, and the released energy is shared between them.
Momentum: mv=MV', so V'=m/Mv.
Total kinetic energy =1/2mv²+1/2MV'²=1/2mv²+1/2M(m²)/(M²)v².
=1/2mv²(1+m/M)=1/2(0.2)v²(1+(0.2)/4)=0.105 v².
0.105 v²=1050 gives v²=10000, so v=100 m s⁻¹.
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