Question

Two particles of masses $1gand2g$, have equal momentum. Find the ratio between their kinetic energies.

Answer 1

Let $m_1=1g$ and $m_2=2g$

Given that

$m_1{v}_1=m_2{v}_2$

$\frac{v_1}{v_2}=\frac{m_2}{m_1}$

$\therefore$ Ratio between their kinetic energies , $=\frac{K_1}{K_2}=\frac{\frac{1}{2}{m}_1{v}_1^2}{\frac{1}{2}{m}_2{v}_2^2}$

$⟹\frac{K_1}{K_2}=\frac{m_1}{m_2}\times \frac{m_2^2}{m_1^2}=\frac{m_2}{m_1}=2$