Answer:1.5
Explanation:
Given
mass of first cart [tex]m_1=6 kg[/tex]
initial Velocity [tex]u_1=3 m/s[/tex]
mass of second cart [tex]m_2=3 kg[/tex]
[tex]u_2=0 m/s[/tex]
In the absence of External Force we can conserve momentum
[tex]m_1u_1+m_2u_2=(m_1+m_2)v[/tex]
[tex]v=\frac{m_1u_1+m_2u_2}{m_1+m_2}[/tex]
[tex]v=\frac{6\times 3+3\times 0}{6+3}[/tex]
[tex]v=2 m/s[/tex]
Final kinetic Energy of two masses
[tex]K.E._2=\frac{1}{2}(m_1+m_2)v^2[/tex]
[tex]K.E._2=\frac{1}{2}\cdot (3+6)\cdot (2)^2[/tex]
[tex]K.E._2=18 J[/tex]
Initial Kinetic Energy
[tex]K.E._1=\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2[/tex]
[tex]K.E._1=\frac{1}{2}6\times 3^2+0[/tex]
[tex]K.E._1=27 J[/tex]
[tex]ratio =\frac{K.E._1}{K.E._2}=\frac{27}{18}=1.5[/tex]
