Three objects A , B and C are kept in a straight line on a...

Three objects $A$ , $B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m$ , $2m$ and $m$ , respectively. The object $A$ moves towards $B$ with a speed $9ms^{- 1}^{}and makes an elastic collision with it. Thereafter,$ 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 $.<br /> <br /> <img alt="" src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fnta_abhyas%252Fjee_main%252Fimages%252FEM0006908_Ques1_1.jpg%3Falt%3Dmedia \text{ and } clean=1 \text{ and } v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2FEM0006908_Ques1_1.jpg?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2FEM0006908_Ques1_1.jpg?alt=media" style="width: 237px; height: 81px;" /></p>$

Options

A $4$
B $7$
C $10$
D $12$

Correct answer

A. $4$

Step-by-step solution

After elastic collision,

{υ}^{'}\text{A} = \left(\dfrac{\text{m} - 2\text{m}}{\text{m} + 2\text{m}}\right)\left(9\right) + \dfrac{2\left(2\text{m}\right)}{\text{m} + 2\text{m}}\left(0\right) = - 3{m s}^{- 1}

Now from conservation of linear momentum after all collisions are complete,

\text{m} \left(+9{m s}^{- 1}\right) = \text{m}\left(-3{m \text{ and } s}^{- 1}\right) + 3\text{m}\left({υ}_{C}\right)<br /><br />or \text{ and } \text{ and }

{υ}_{C} = 4{m s}^{- 1}

</br?>

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