skolepikegq9s

2023-02-21

Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball 2. Initially, ball 1 moves with a speed u towards ball 2 which is at rest. Immediately after the collision, ball 1 travels at a speed of $\frac{u}{3}$ in the same direction. What type of collision has occurred?
A)Inelastic;
B)Elastic;
C)Completely inelastic;
D)cannot be determined from the information

Kamari Potts

The correct answer is B Elastic
Let mass of ball 1=2m
Mass of ball 2=m
Velocity of ball 1 before collision =u
Velocity of ball 1 after collision $=\frac{u}{3}$
Velocity of ball 2 before collision =0
Let final velocity of ball 2$={v}_{2}$
Momentum will be conserved because there is no outside force acting on the system.
Prior to and following a collision, using conservation of linear momentum.
$\left(2m\right)u+m\left(0\right)=\left(m\right){v}_{2}+\left(2m\right)\left(\frac{u}{3}\right)$
or ${v}_{2}=\frac{4u}{3}$
Now,
$e=\frac{\text{velocity of separation}}{\text{velocity of approach}}\phantom{\rule{0ex}{0ex}}e=\frac{{v}_{2}-{v}_{1}}{{u}_{1}-{u}_{2}}\phantom{\rule{0ex}{0ex}}e=\frac{\frac{4u}{3}-\frac{u}{3}}{u-0}=1$
Thus, collision is elastic.

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