Find the ratio of the linear momenta of two particles of masses 1.0 kg and 4.0 kg if their kinetic energies are equal.

Explanation

Let the mass of the two particle be `m_1,m_2` respectively
`m_1=1kgm_2=4kg`
`:.` According to question
`(1/2)m_1v_2^2=(1/2)m_2v_2^2`
`rarr m_1/m_2=v_2^2/v_1^2`
`rarr v_2/v_1=sqrt(m_1/m_2)`
`rarr v_1/v_2=(sqrt(m_2/m_1)`
`Now, (m_1v_1)/(m_2v_2)=m_1/m_2 sqrt(m_2/m_1)`
`=sqrt(m_1/m_2)=sqrt(1/4)=1/2`
`rarr (m_1v_1)/(m_2v_20=1:2`