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In an elastic collision of two bodies , ...

In an elastic collision of two bodies , the momentum and energy of each body is conserved .

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No , In this case total kinetic energy is not conserved because when the bodies are in contact in elastic collision even the kinetic energy is converted into potential energy .
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KUMAR PRAKASHAN-WORK, ENERGY AND POWER -SECTION - B Numericals (Numerical From Textual Exercise)
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