Question

A bomb of mass 9 kg explodes into the 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(a) 96 (b) 384(c) 192 (d) 768

Answer 1

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

So, option C is correct

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Answer 2

Question:

A bomb of mass 9 kg explodes into two pieces of 3 kg and 6 kg the velocity of 3 kg pieces 16 m per second the kinetic energy of 6 kg piece is.

Answer:

When the bomb explodes into two pieces then:

Mass of one part (m1)= 3kg

Velocity of that part (v1)= 16m/s

Mass of another part (m2)= 6kg

Velocity of another part (v2)= ?  

By the conservation of linear momentum;

        m1 * u1 +m2 * u2 = m1 * v1 + m2 * v2

m1 * v1 + m2 * v2 = 0

m1 * v1 = -m2 * v2  

So taking magnitude only:

m1 * v1 = m2 * v2

3 * 16 = 6 * v2

v2 = 8 m/s

Now, kinetic energy (KE2) = 1/2 (m2 *v2²)

=0.5 * 6 * 8²

= 3 * 64

=192 joule s

Hence the KE of of 6kg mass is 192 joules