TS EAMCET · Physics · Center of Mass Momentum and Collision
Two objects of masses \(200 \mathrm{~g}\) and \(500 \mathrm{~g}\) possess velocities \(10 \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\) and \(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}\) respectively. The velocity of their centre of mass in \(\mathrm{m} / \mathrm{s}\) is :
- A \(5 \hat{\mathbf{i}}-25 \hat{\mathbf{j}}\)
- B \(\frac{5}{7} \hat{\mathbf{i}}-25 \hat{\mathbf{j}}\)
- C \(5 \hat{\mathbf{i}}+\frac{25}{7} \hat{\mathbf{j}}\)
- D \(25 \hat{\mathbf{j}}-\frac{5}{7} \hat{\mathbf{j}}\)
Answer & Solution
Correct Answer
(C) \(5 \hat{\mathbf{i}}+\frac{25}{7} \hat{\mathbf{j}}\)
Step-by-step Solution
Detailed explanation
\(m_1=200 \mathrm{~g}, m_2=500 \mathrm{~g}\) \(v_1=10 \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}, v_2=(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}\) velocity of centre of mass, \(v_{\mathrm{CM}}=\frac{m_1 v_1+m_2 v_2}{m_1+m_2}\)…
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