A moving mass of 8 kg collides elastically with a...

A moving mass of $8 \mathrm{~kg}$ collides elastically with a stationary mass of $2 \mathrm{~kg}$. If $\mathrm{KE}$ be the initial kinetic energy of the moving mass, the kinetic energy left with it after the collision will be (a) $0.08 \mathrm{KE}$ (b) $0.36 \mathrm{KE}$ (c) $0.64 \mathrm{KE}$ (d) $0.80 \mathrm{KE}$

A moving mass of $8 \mathrm{~kg}$ collides elastically with a stationary mass of $2 \mathrm{~kg}$. If $\mathrm{KE}$ be the initial kinetic energy of the moving mass, the kinetic energy left with it after the collision will be
(a) $0.08 \mathrm{KE}$
(b) $0.36 \mathrm{KE}$
(c) $0.64 \mathrm{KE}$
(d) $0.80 \mathrm{KE}$

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Key Concepts

Elastic Collision

An elastic collision is a type of collision in which both momentum and kinetic energy are conserved. In such collisions, the objects rebound without any loss of kinetic energy to sound, heat, or deformation, making the mathematical analysis straightforward using conservation laws.

Conservation of Momentum

The conservation of momentum is a fundamental principle which states that the total momentum of a closed system remains constant before and after a collision, regardless of the nature of the collision. This principle is key in analyzing the motion of colliding objects, particularly in collisions involving objects with different masses.

Conservation of Kinetic Energy

In elastic collisions, not only is momentum conserved, but kinetic energy is also conserved. This means that the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. This concept is critical when solving problems involving collisions, as it provides an additional equation to determine post-collision velocities and energy distributions.

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