Answer:
The correct option is;
D. The kinetic energy decreases by 3·m₀·v₀²
Explanation:
The given parameters are;
The mass of object X = m₀
The initial velocity of object X = v₀
The mass of object Y = 2·m₀
The initial velocity of object Y = -2·v₀
By conservation of linear momentum, we have;
The total initial momentum = The total final momentum
Therefore, we have;
The total initial momentum = m₀·v₀ - 2·m₀·2·v₀ = The total final momentum
∴ The total final momentum = -3·m₀·v₀
The total mass of the two object after sticking together = 2·m₀ + m₀ = 3·m₀
Therefore, the velocity of the two objects after collision = (The total final momentum)/(Total mass) = -3·m₀·v₀/(3·m₀) = -v₀
The kinetic energy = 1/2 × Mass × (Velocity)²
Therefore, the kinetic energy after collision = 1/2 × (3·m₀) × v₀² = 3·m₀·v₀²/2
The kinetic energy before collision = 1/2 × m₀ × v₀² + 1/2 × (2·m₀) × (2·v₀)² = (1/2 + 4) × (m₀·v₀²)
∴ The kinetic energy before collision = 9·(m₀·v₀²)/2
The change in kinetic energy = The kinetic energy after collision - The kinetic energy before collision = 3·m₀·v₀²/2 - 9·(m₀·v₀²)/2 = -3·m₀·v₀²
Therefore, the kinetic energy decreases by 3·m₀·v₀².
