Momentum and CollisionHardBloom L3
Question
A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle which has twice its mass during the impact.
Options
A.The minimum kinetic energy of the system is 1 joule.
B.The maximum elastic potential energy of the system is 2 joule.
C.Momentum and total kinetic energy of the system are conserved at every instant.
D.The ratio of kinetic energy to potential energy of the system first decreases and then increases.
Solution
Sol. 
Maximum compression (RE ⇒ Max ⇒ KE ⇒ Min)
3mvC = mv1
⇒ vC = $\frac{v_{1}}{3}$
$\frac{1}{2}mv_{1}^{2} = 3$, ${(KE)\frac{1}{2}_{C}^{2}\frac{3}{2}\left( \frac{v_{1}}{3} \right)^{2}\frac{1}{6}_{1}^{2}\frac{1}{3}\left( \frac{1}{2}mv_{1}^{2} \right)\frac{1}{3}}_{\min}$
⇒ (KE)min = 1J
(PE)max = 3 – 1 = 2J
(C) P ⇒ Always conserved
KE ⇒ During collision charges
PE↑ & KE↓ ⇒ $\left( \frac{PE}{KE} \right) \uparrow \Rightarrow \frac{KE}{PE} \downarrow$
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