Q.Which is conserved in an inelastic collision? Total energy (or) Kinetic energy?

Inelastic Collision – From Intuition to Precision

Imagine two lumps of clay. You throw one at the other, and they smack together, stick, and move off as one blob. That's the classic inelastic collision. Something is clearly lost — the sound of the impact, a little heat from the deformation, and the fact that the clay is now squished. That "something lost" is kinetic energy. But here's the key: the total momentum of the two lumps before the crash is exactly the same as the momentum of the single combined lump after the crash. Momentum is always conserved in any collision if no external force acts. Energy, however, can change form.

The most extreme version is a perfectly inelastic collision, where the objects stick together after impact. That's the clay example. But not all inelastic collisions are that dramatic. A car crash is inelastic — the cars crumple, metal bends, heat radiates — but they usually don't fuse into one piece. The defining feature is simply that kinetic energy is not the same before and after.

The Precise Statement

For any two objects colliding inelastically (with no external forces):

Momentum conservation:

Kinetic energy is NOT conserved:

The "lost" kinetic energy appears as heat, sound, or deformation energy. You cannot write an equation that sets the initial KE equal to the final KE — that would be an elastic collision.

Why Does This Happen?

When two objects collide, forces between them do work. In an elastic collision, that work is stored and released like a spring — no permanent change. In an inelastic collision, the material deforms permanently. The work done to squash the clay or crumple the metal is not recovered as motion; it dissipates as heat. That's why the final kinetic energy is less.

A Common Exam Trap

Students often try to "conserve energy" in an inelastic collision by writing:

This is wrong for an inelastic collision. That equation would only hold if no energy were lost — which is the definition of an elastic collision. In a perfectly inelastic collision, the correct relation is only the momentum equation above. The kinetic energy after is always less.

Quick Example

A 2 kg ball moving at 3 m/s hits a stationary 1 kg ball and they stick together. Find the final speed.

Momentum before: $2 \times 3 + 1 \times 0 = 6$ kg m/s

Momentum after: $(2+1)v = 3v$

Set equal: $3v = 6 \implies v = 2$ m/s

Kinetic energy before: $\frac12 (2)(3^2) = 9$ J

Kinetic energy after: $\frac12 (3)(2^2) = 6$ J

Lost: 3 J — turned into heat and deformation.

Final answer: The final speed is 2 m/s, and 3 J of kinetic energy is lost.

Inelastic collisions are covered in the same NCERT Class 11 Physics chapter as elastic collisions, and are commonly searched as "inelastic collision examples class 11 physics" or "elastic vs inelastic collision important questions CBSE and JEE".