Three particles of masses 10;g, 20;g and 40;g | vedclass

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(D) According to the law of conservation of linear momentum,the total initial momentum of the system is equal to the total final momentum.Initial mome

Vedclass · Accepted Answer

$\hat{i} + 3\hat{j} + 10\hat{k}$

Vedclass · Answer

(D) According to the law of conservation of linear momentum,the total initial momentum of the system is equal to the total final momentum.Initial momentum: $\vec{P}_i = m_1\vec{u}_1 + m_2\vec{u}_2 + m_3\vec{u}_3$$\vec{P}_i = 10(10\hat{i}) + 20(10\hat{j}) + 40(10\hat{k}) = 100\hat{i} + 200\hat{j} + 400\hat{k}$Final momentum: $\vec{P}_f = m_1\vec{v}_1 + m_2\vec{v}_2 + m_3\vec{v}_3$Given $\vec{v}_1 = 0$ and $\vec{v}_2 = (3\hat{i} + 4\hat{j})\;m/s$.$\vec{P}_f = 10(0) + 20(3\hat{i} + 4\hat{j}) + 40\vec{v}_3 = 60\hat{i} + 80\hat{j} + 40\vec{v}_3$Equating $\vec{P}_i = \vec{P}_f$:$100\hat{i} + 200\hat{j} + 400\hat{k} = 60\hat{i} + 80\hat{j} + 40\vec{v}_3$$40\vec{v}_3 = (100 - 60)\hat{i} + (200 - 80)\hat{j} + 400\hat{k}$$40\vec{v}_3 = 40\hat{i} + 120\hat{j} + 400\hat{k}$$\vec{v}_3 = \hat{i} + 3\hat{j} + 10\hat{k}\;m/s$.

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