Three objects A, B and C are kept in a straight line on a frictio… - Vidyadip

Question

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 $9 \mathrm{~m} / \mathrm{s}$ 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 $\mathrm{m} / \mathrm{s}$ ) of the object $\mathrm{C}$.

✓

Answer

After $1$ st collision

$mv _{ A }= mv _{ A }^{\prime}+2 mv _{ B }^{\prime}$

$-1=\frac{ v _{ B }^{\prime}- v _{ A }^{\prime}}{ o - v _{ A }} \Rightarrow v _{ B }^{\prime}=6 \ m / s$

After the and collision

$2 m v_{ B }^{\prime}=(2 \ m + m ) v _{ C } \Rightarrow v _{ C }=\frac{2}{3} v _{ B }^{\prime} \Rightarrow v _{ C }=4 \ m / s$

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