Centre of Mass 3 Question 28
31. Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m, 2 m$ and $m$, respectively. The object $A$ moves towards $B$ with a speed $9 ms^{-1}$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$. All motions occur on the same straight line. Find the final speed (in $ms^{-1}$ ) of the object $C$.
(2009)
Analytical & Descriptive Questions
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Answer:
Correct Answer: 31.4
Solution:
- After elastic collision,
$$ v _A^{\prime}=\frac{m-2 m}{m+2 m}(9)+\frac{2(2 m)}{m+2 m}(0)=-3 ms^{-1} $$
Now, from conservation of linear momentum after all collisions are complete,
$$ m\left(+9 ms^{-1}\right)=m\left(-3 ms^{-1}\right)+3 m\left(v _C\right) \text { or } v _C=4 ms^{-1} $$
