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4.1 , newtons laws of motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics4.1 , newtons laws of motion1 Mark
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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