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  4. In an elastic collision between two bodies. the physical quantity that is conserved is:

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Q. In an elastic collision between two bodies. the physical quantity that is conserved is:

EAMCETEAMCET 1999

Solution:

A collision is said to be elastic if the total kinetic energy before and after collision remain the same or KE is conserved. Thus, if two bodies of masses $ {{m}_{1}} $ and $ {{m}_{2}} $ moving with velocities $ {{u}_{1}} $ and $ {{u}_{2}} $ collide in absence of external force also elastically and $ {{v}_{1}} $ and $ {{v}_{2}} $ are the final velocities, then according to conservation of momentum $ {{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}} $ Also, according to principle of conservation of KE $ \frac{1}{2}mu_{1}^{2}+\frac{1}{2}mu_{2}^{2}=\frac{1}{2}mv_{1}^{2}+\frac{1}{2}mv_{2}^{2} $ Therefore, it is clear that both kinetic energy and momentum are conserved.