Final answer:
To determine how much original energy the 5 kg mass obtains in an inelastic collision, conservation of momentum is used to find the final velocity, after which the kinetic energy before and after collision is compared to derive the energy percentage obtained by the larger mass.
The correct answer is none of these.
Step-by-step explanation:
The question relates to the conservation of energy and momentum in physics, more specifically, to a problem involving an inelastic collision where two masses stick together after the collision. To determine how much of the original energy the 5 kg mass obtains, we can use the principle of conservation of momentum to find the final velocity of the combined masses and then calculate the kinetic energy before and after the collision.
Momentum before collision = momentum after collision: (2.5 kg)(initial velocity) = (2.5 kg + 5 kg)(final velocity). Let's assume the initial velocity is v. The final velocity of both masses sticking together would therefore be (2.5 kg * v) / (7.5 kg).
Initial kinetic energy (KE) of the 2.5 kg mass = 0.5 * 2.5 kg * v2, and the final KE of the combined mass is 0.5 * (2.5 kg + 5 kg) * [(2.5 kg * v) / (7.5 kg)]2. The ratio of the final KE to the initial KE will give us the percentage of the original energy obtained by the 5 kg mass.