Question

A bomb of mass 9 kg at rest explodes into two pieces of masses 3 kg and 6 kg. the velocity of mass 3 kg is 16 ms–1. the kinetic energy of mass 6 kg is

Answer 1

By conservation of linear momentum

Velocity of 6 kg mass = -mu/m’
= -(3 kg × 16 m/s) / (6 kg)
= - 8 m/s
[-ve sign indicates that velocity is in the direction opposite to that of 3 kg mass]

Kinetic energy of 6 kg mass is
K = 0.5 mv^2
= 0.5 × 6 kg × (8 m/s)^2
= 192 Joule

Kinetic energy of 6 kg mass is 192 Joule

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