Question

A stationary object explodes into masses $m_1$ and $m_2$. They move in opposite directions with velocities $V_1$ and $V_2$. The ratio of kinetic energy $E_1$ to kinetic energy $E_2$ is.

• A. $\frac{m_2}{m_1}$
• B. $\frac{m_1}{m_2}$
• C. $\frac{2m_2}{m_1}$
• D. $\frac{2m_1}{m_2}$

Answer 1

The correct option is A $\frac{m_2}{m_1}$

As the initial momentum of the system is zero, thus according to the conservation of linear momentum final momentum of the system must also be zero.

So, magnitude of momentum of mass $m_1$ must be equal to that of mass $m_2$ i.e. $m_1{V}_1=m_2{V}_2$ Or $p_1=p_2$

Kinetic energy of mass $m_1$, $E_1=\frac{p_1^2}{2m_1}$

Kinetic energy of mass $m_2$, $E_2=\frac{p_2^2}{2m_2}$

Thus ratio of kinetic energy $\frac{E_1}{E_2}=\frac{p_1^2/2m_1}{p_2^2/2m_2}$ (using $p_1=p_2$)

$⟹$ $\frac{E_1}{E_2}=\frac{m_2}{m_1}$