IGNOU PHE 1 BPHE 101 2026 - A particle of mass , initially moving with a velocity of &nb

Question

A particle of mass $4.0\text{ kg}$ , initially moving with a velocity of $5.0\text{ ms}^{-1}$ collides elastically with a particle of mass $6.0\text{ kg}$ , initially moving with a velocity of $-8.0\text{ ms}^{-1}$ . What are the velocities of the two particles before and after the collision in the centre of mass frame of reference? What are the velocities of the two particles after the collision in the laboratory frame?

10 Feb 2026

Answer :

Word Count : 239

In the center of mass (CM) frame of reference, the velocities of the two particles before and after the collision can be determined by first calculating the velocity of the center of mass (V_cm). For two particles of masses ( m_1 ) and ( m_2 ), with initial velocities ( v_1 ) and ( v_2 ) in the laboratory frame, the velocity of the center of mass is given by: [ V_{\text{cm}} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} ] In the CM frame, the velocity of each particle is measured relative

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