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A light body and a heavy body have the s...

A light body and a heavy body have the same kinetic energy. Which one will have greater momentum?

Text Solution

Verified by Experts

Given data `E_1 - E_2`
`1/2 m_1v_1^2 = 1/2 m_2v_2^2`
or ` (v_2^2)/(v_1^2) = m_1/m_2 " or " v_2/v_1 = sqrt(m_1/m_2)`
As `P_2 = m_2v_2" and " P_1 = m_1v_1`
`P_2/P_1 = (m_2v_2)/(m_1v_1) = m_2/m_1 sqrt(m_1/m_2) = sqrt( (m_2^2 m_1)/(m_1^2 m_2))`
` = P_2/P_1 = sqrt(m_2/m_1) , ` if ` m_2 gt m_1`
then `P_2 gt P_1`
i.e. a heavier body has greatest linear momentum
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