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

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. The initial velocity of the shell is :

Let the initial velocity of the shell be v, then by the conservation of momentum mv = Mv'
where v' = velocity of gun.

∴ v' =		m		v
		M

Now, total K.E. =	1	mv² +	1	Mv'²
	2		2

=	1	mv² +	1	M		m		²	v²
	2		2			M

=	1	mv²		1 +	m
	2				M

=			1	× 0.2			1 +	0.2		v² = (0.1 × 1.05)v²
			2					4

But total K.E. = 1.05 kJ = 1.05 × 10³ J
∴ 1.05 × 10³ = 0.1 × 1.05 × v²

v² =	1.05 × 10³	= 10⁴
	0.1 × 1.05

∴ v = 10² = 100 ms^–1.