Work Energy And Power Question 297

Question: A collision occurs between two identical balls of mass m each, moving with velocity $ {{\overrightarrow{\mu }}_1}and{{\overrightarrow{\mu }}_2} $ . If the collision is head on and the energy lost in the collision is $ \Delta E=\frac{3}{16}{{({{\vec{u}}_1}-{{\vec{u}}_2})}^{2}} $ then the coefficient of restitution is

Options:

A) 0.25

B) 0.75

C) 0.5

D) 0.9

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Energy lost in the collision is $ \Delta E=\frac{1}{2}mu^2 _{red}( 1-e^{2} ) $
$ \therefore \frac{3}{16}{{( {{{\vec{u}}}_1}-{{{\vec{u}}}_2} )}^{2}}=\frac{1}{2}mu^2 _{rel}( 1-e^{2} )\Rightarrow e=0.5 $



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