A shell of mass m is at rest initially. It explodes into three fr… - Vidyadip

MCQ

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2: 2: 1$. If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is :

A
$\sqrt{2} v$
✓
$2 \sqrt{2} v$
C
$3 \sqrt{2} v$
D
$v$

✓

Answer

Correct option: B.

$2 \sqrt{2} v$

b
By conservation of momentum :

$m(0)=\frac{2 m}{5}(-v \hat{i})+\frac{2 m}{5}(-v \hat{j})+\frac{m}{5} \vec{v}^{\prime}$

$\Rightarrow \vec{v}^{\prime}=2 v \hat{i}+2 v \hat{j}$

$\Rightarrow v^{\prime}=\sqrt{(2 v)^{2}+(2 v)^{2}}$

$=2 \sqrt{2} v$

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