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A bomb of mass 9 kg explodes into 2 pieces of masses 3 kg and 6 kg .The velocity of mass 3 kg is 16 m/s.The kinetic energy of mass 6 kg in joule is what?

A bomb of mass 9 kg explodes into 2 pieces of masses 3 kg and 6 kg .The velocity of mass 3 kg is 16 m/s.The kinetic energy of mass 6 kg in joule is what?

Grade:11

2 Answers

mohammad husain
17 Points
6 years ago
given  mass of the bomb ,M=9kg
           initial value of the bomb=0m/s
           mass of smaller fragmet  =3kg=m1  (let)
            velocity of the smaller part just after explosion=16m/s
           mass of the bigger fragmet =6kg=m2 (let)
             let, velocity of the bigger part just after explosion= v      
          as there is no external force is acting on the bomb intially
                so the momentum is conserved in all direction
             i.e      P(just after explosion)=P(just before explosion )
                           m1*16 + m2*v = M*0
                       =>  v = -8m/s
    so the kinetic energy of the fragment of mass 6kg = (1/2)*m2*v*v Joule
                                                                                   =(1/2)*6*64
                                                                                   =192 Joule
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

Given, m1=3kg , m2 = 6kg , v1 = 16m/s , K.E 2 = ?
According to law of conservation of momentum :
(m1 × v1) + (m2 × v2) = (m1 + m2) ×v
(3×16) + (6×(-v2)) = (3+6) × 0
( -v2 because both are moving in opposite directions
48 - (6 × v2) = 0
48 = 6 ×v2
therefore, v2 = 8m/s
K.E2 = 1/2 × m2 × v2 square
= 1/2 ×6 x 8 square
= 3 × 64
= 192J

Thanks and Regards

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