Question

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

Answer 1

Dear Student ,
$$\begin{gathered} Hereinthiscasewecanwritethat, \\ Letthemassofthelightobjectbe{m}_{1}andvelocitybe{v}_{2}andthemassandvelocityoftheheavyobjectbe{m}_{2}and{v}_2. \\ Given,m_1{v}_1=m_2{v}_2 \\ \Rightarrow \frac{m_1}{m_2}=\frac{v_2}{v_1}....\left(1\right) \\ Nowasweknowthatkineticenergyis, \\ \frac{E_1}{E_2}=\frac{{\displaystyle \frac{1}{2}}{m}_1{v_1}^2}{{\displaystyle \frac{1}{2}}{m}_2{v_2}^2} \\ Nowfromequationwecanwritethat, \\ \frac{E_1}{E_2}=\frac{{\displaystyle v_1}}{{\displaystyle v_2}}=\frac{m_2}{m_1}>1\left[m_2>m_1\right] \\ \Rightarrow E_1>E_2. \\ Sokineticenergyofthelighterobjectwillbelarger. \end{gathered}$$

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