A mass m moving horizontally (along the x- axis) with velocity v … - Vidyadip

MCQ

A mass $m$ moving horizontally (along the $x-$ axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y-$ axis) with velocity $2v$. The final velocity of the combination is

A
$\frac{3}{2}\,v\hat i + \frac{1}{4}\,v\hat j$
✓
$\frac{1}{4}\,v\hat i + \frac{3}{2}\,v\hat j$
C
$\frac{1}{3}\,v\hat i + \frac{2}{3}\,v\hat j$
D
$\frac{2}{3}\,v\hat i + \frac{1}{3}\,v\hat j$

✓

Answer

Correct option: B.

$\frac{1}{4}\,v\hat i + \frac{3}{2}\,v\hat j$

b
By conservation of linear momentum

$4 m \vec{v}_{c}=m v \hat{i}+3 m(2 v \hat{j}) \Rightarrow \vec{v}_{c}=\frac{v}{4} \hat{i}+\frac{3}{2} v \hat{j}$

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