Question

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

• A. $\frac{u}{12}(\hat{i}+\sqrt{3}\hat{j})$
• B. $\frac{u}{12}(\hat{i}-\sqrt{3}\hat{j})$
• C. $\frac{u}{12}(-\hat{i}+\sqrt{3}\hat{j})$
• D. $\frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})$

Answer 1

The correct option is D $\frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})$

Applying conservation of momentum along the x-axis,

$m\left(3u\right)-2m\left(2ucos60\right)-3m\left(ucos60\right)$ = $6m\left(v_x\right)$

$v_x=\frac{-u}{12}$

Similarly, along y-axis,

$3musin60-4musin60=6mu\left(v_y\right)$

$v_y=\frac{-3^{0.5}u}{12}$