A particle of mass $m_1$ is moving with a velocity $v_1$ and another particle of mass $m_2$ is moving with a…
A particle of mass $m_1$ is moving with a velocity $v_1$ and another particle of mass $m_2$ is moving with a velocity $v_2$. Both of them have the same momentum but their different kinetic energies are $E_1$ and $E_2$ respectively. If $m_1 > m_2$ then:
$E_1 < E_2$
$\frac{E_1}{E_2}=\frac{m_1}{m_1}$
$E_1 > E_2$
$E_1=E_2$
Solution
We know that K.E. $=\frac{P^2}{2 m}$
$\begin{array}{ll}
\therefore & \frac{E_1}{E_2}=\frac{P_1^2 / 2 m_1}{P_2^2 / 2 m_2} \\
\Rightarrow \quad \frac{E_1}{E_2}=\frac{m_2}{m_1}
\end{array}$
Here $\quad m_1=m_2$
$\therefore \quad E_1 < E_2$
.