Question

Question 21
A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?

Answer 1

$p_1=m_1{v}_1$ $p_1=m_2{v}_2$
But $p_1=p_2$ or $m_1{v}_1=m_2{v}_2$

If $m_1<m_2$ then $v_1>v_2$
$\begin{array}{cc}(K.E{)}_1=\frac{1}{2}{m}_1{v}_1^2& (K.E{)}_2=\frac{1}{2}{m}_2{v}_2^2\\ (K.E{)}_1=\frac{1}{2}(m_1{v}_1)v_1=\frac{1}{2}{p}_1{v}_1& (K.E{)}_2=\frac{1}{2}(m_2{v}_2)v_2=\frac{1}{2}{p}_2{v}_2\end{array}$

considering $p_1=p_2$
$\frac{(K.E{)}_1}{(K.E{)}_2}=\frac{\frac{1}{2}{p}_2{v}_1}{\frac{1}{2}{p}_2{v}_2}=\frac{v_1}{v_2}$

But $v_1>v_2$
Therefore, $(K.E{)}_1>(K.E{)}_2$