# Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u, and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be : Option 1) Option 2) Option 3) Option 4)

As we learnt in

Law of Consevation of Momentum -

$\vec{F}=\frac{\vec{dp}}{dt}$

$\vec{F}=0$            then $\vec{p}=constant$

$\vec{p}=\vec{p}_{1}+\vec{p}_{2}+\cdots =const$

- wherein

$\ast$ Independent of frame of reference

Pi = Py

$m3u\hat{i}+3m[-ucos60\hat{i}+usin60\hat{j}]+2m[-2ucos60\hat{i}-2usin60\hat{j}]$

$=3mu\hat{i}+3m[\frac{-v}{2}\hat{i}+\frac{0\sqrt{3}\hat{j}}{2}]\Rightarrow \frac{u}{12}(\hat{-i}-\sqrt{3}\hat{j})$

Option 1)

Incorrect

Option 2)

Incorrect

Option 3)

Incorrect

Option 4)

Correct

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