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Question

A stationary body explodes into three fragments of masses m1,m2 and m3. If momentum of one fragment is p and one fragment of mass m3 remains at rest, the energy of explosion is:


A
p22(m1+m2)
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B
p22m1m2
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C
p2(m1+m2)2m1m2
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D
p22(m1m2)
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Solution

The correct option is B p2(m1+m2)2m1m2
Let, p be the momentum of one fragment with mass m1 and p be the momentum of other fragment with mass m2,
The energy of explosion is

KE=12m1(v1)2+12m2(v2)2

KE=12m1(m1)2(v1)2+12m2(m2)2(v2)2

KE=12m1p21+12m2p22

KE=2(m2p21+m1p22)4m1m2

Since, after explosion momentum will be conserved hence, p=p1=p2

KE=m2p2+m1p22m1m2

KE=p2(m1+m2)2m1m2

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