Question

Two bodies of masses 3 kg and 2 kg collide bead-on. Their relative velocities before and after collision are 20 m/s and 5 m/s respectively. The loss of kinetic energy of the system is ______.

Options

• 120 J

• 100 J

• 80 J

• 225 J

Answer 1

Two bodies of masses 3 kg and 2 kg collide bead-on. Their relative velocities before and after collision are 20 m/s and 5 m/s respectively. The loss of kinetic energy of the system is 225 J.

Explanation:

Say mass of 2 kg is at rest initially, then

`3 xx 20 + 2 xx 0 = 3"v"_1 + 2"v"_2`

`therefore 60 = 3"v"_1 + "V"_2` ....(i)

`therefore "e" =5/20 =1/4`

`therefore ("V"_2 - "V"_1)/(20 - 0) = 1/4`

`therefore 20 = 4"V"_2 - 4"V"_1` ....(ii)

Solving equations (i) and (ii),

V₁ = 10 , V₂ = 15

`therefore ` Loss of kinetic energy

` = 1/2 xx 3 xx 20^2 - 1/2 xx 3 xx 10^2 -1/2 xx 2 xx 15^2`

= 225 J