Question

A stationary particle explodes into two particles of masses $m_{1}\ and\ m_{2}$ which move in opposite directions with velocities $v_{1}\ and\ v_{2}$. The ratio of their kinetic energies $\frac{E_{1}}{E_{2}}$ is
(a) ${m_{1}v_{2}}/{m_{2}v_{1}}$(b) ${m_{2}}/{m_{1}}$(c) ${m_{1}}/{m_{2}}$
(d) 1

Answer 1

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Answer 2

Answer:

B) m2/m1

Explanation:

Mass of particle = m1 and m2 ( Given)

According to the law of conservation of energy, the final momentum after the explosion is equal to the initial momentum.

Thus, m₁v₁ + m₂v₂ = (m₁+m₂)V

Since, initially the particle was static, V = 0 and as v₁ and v₂ is opposite in direction,

m₁v₁ - m₂v₂ = 0

or, m₁v₁ = m₂v₂

or, (m₁v₁)² = (m₂v₂)²

or, (1/2)m₁²v₁² = (1/2)m₂²v₂²

or, E₁.m₁ = E₂.m₂

or, E₁ / E₂ = m₂ / m₁

Thus, the ratio of kinetic energies E1/E2 will be m2/m1