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Q.
The coefficient of restitution $e$, for a perfectly elastic collision is
AIPMTAIPMT 1988Work, Energy and Power
Solution:
Coefficient of restitution or resilience of two bodies is defined as the constant ratio of relative velocity after impact to the relative velocity of the bodies before impact when the two bodies collide head on.
There velocities are in the opposite directions.
Thus $\frac{v_{1}-v_{2}}{u_{1}-u_{2}}=$ constant $=- e$
The constant $e$ is known as coeff. of restitution or resilience of two bodies.
For a perfectly elastic collision, $e=1$ and for a perfectly inelastic collision, $e=0$.
Thus $0 \leq e \leq 1$.