Question

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. the velocity of 18 kg mass is 6 ms–1. the kinetic energy of the other mass is

Answer 1

By using conservation of linear momentum
Velocity of 12kg body comes out to be -9m/s
Therefore KE=486joules

Answer 2

Answer:

Kinetic energy of the other mass is 486 J.

Explanation:

[Method 1]

Since the object was initially at rest the momentum was zero. So, according to the conservation of momentum, the final momentum will remain the same i.e. Pi = Pf = 0

Now, since Pf = 0, we have; (after explosion)

      m₁v₁ +m₂v₂ = 0

Let 18 kg mass be m₁, 12 kg mass be m₂, velocity of 18 kg mass be v₁ and that of other's be v₂. Putting the given values in the formula, we get;-

    18 × 6 + 12 × v₂ = 0

       18 × 6 = - 12 × v₂

            v₂ = - 9 m/s

Now, we also know that;-

      K.E. = 1/2 mv²

Putting the given values for the kinetic energy of the 12 kg mass;

      K.E. = 1/2 × 12 × 9×9 (since energy can't be negative)

      K.E. = 6 × 81

     K.E. = 486 J

[Method 2]

Since,  

               K.E. = ρ²/ 2m

Hence,

               K.E. = (18 ×6)²/ 2 × 12

[note; we put ρ = 18 ×6 as ρ₁ = ρ₂ for the two particles]

               K.E. = 486 J

Hope it helps! ;-))