Question

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

Answer 1

initial momentum of bomb is 0 

after exploding the speed of mass 18 kg is 6 m/s and the speed of mass 12 be U

 

so momentum after collision = momentum 1 + momentum 2

P = 18 x 6 + 12 x U

P = 108 + 12 U

now according to conservation of momentum

momentum before collision = momentum after collision

o = 108 + 12 U

-108 = 12U

-108/12 = U

-9 = U

  

so KE = 1/2 m v square

KE = 1/2 x 12 x -9 square

KE = 486 J

Answer 2

Question:

A bomb of mass 30 kg at rest explodes into 2 pieces of masses 18 kg and 12 kg the velocity of 18 kg mass is 6 m/s the KE of the other mass will be ?

Answer:

486 J

Explanation:

The linear momentum of the exploding part will remain conserved.

Applying Conservation of linear momentum,

m₁u₁ = m₂u₂

here,

m₁ = 18 kg

m₂ = 12 kg

u₁ = 6 m/s

u₂ = ?

u₂ = 18×6÷12 = 9 m/s

u₂ = 9 m/s

Now, The kinetic energy of 12 kg mass

K.E₂ = m₂u₂²/2 = 12×(9)²/2 = 6×81 = 486 J