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A body of mass 1.0 kg strikes elastically with another body at rest and continues to move in the same direction with one-fourth of its initial velocity. The mass of the other body is |
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Answer» 0.6 kg  According to the law of convervation of LINEAR MOMENTUM , we get `m_1 u_1 + m_2 xx 0 = m_1 v_1 + m_2v_2` or `m_1 u_1 = m_1 xx (u_1)/(4) + m_2v_2 " or " m_2v_2 = 3/4 m_1u_1 ""….(i)` According to the law of conservation of kinetic energy, we get `1/2 m_1 u_1^2 + 1/2 m_2 xx 0^2 = 1/2 m_1v_1^2 + 1/2 m_2v_2^2` or `m_2v_2^2 = 15/16 m_1u_1^2 "".....(ii)` Divide (ii) by (i), we get `(m_2 v_2^2)/(m_2v_2) = (15/16 m_1 u_1^2)/(3/4 m_1 u_1) " or " v_2 = 5/4 u_1` On substituting this value of `v_2` in (i), we get `m_2 5/4 u_1 = 3/4 m_1 u_1 " or " m_2 = 3/5 m_1 = 3/5 xx 1.0 kg = 0.6 kg`. |
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