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for example when two objects undergo a collision and no external force is acting on them. Will both kinetic energy and momentum be conserved or just momentum?

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The momentum will be conserved in all cases when you consider the whole interacting system.

The total energy of the colliding bodies will also be conserved. But kinetic energy will only be conserved if the collision is elastic. It's not conserved as usually the collisions are inelastic where a bit of energy ends up as sound waves. If the bodies rub against each other during collision a bit of the energy will be also be lost as heat and a bit of energy will turn into heat if the bodies deform. The energy can be converted into other forms as well depending upon the situation.

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  • $\begingroup$ i still dont get this.. if some KE is lost from the system of the balls as heat or sound, then that's the same as saying some of the system's $\frac{1}{2}mv^2$ is lost right?. then how can the system's $mv$ remain constant? $\endgroup$
    – Hisham
    Oct 30 '19 at 18:12
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    $\begingroup$ @UbaidHassan Remember I said the entire interacting system. Not just the system of interest. Air particles can vibrate (sound) while some other interacting particles can exchange momentum in the form of heat. $\endgroup$ Oct 30 '19 at 18:20
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If all the momentum is in one body you have more energy than if it is shared between two.

Try it with some simple numbers - say both masses = 1 and either two velocities both = 1 or one velocity = 2.

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