Search any question & find its solution
Question:
Answered & Verified by Expert
A stationary particle explodes into two particles of masses $m_1$ and $m_2$ which more in opposite direction with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $E_1 / E_2$ is:
Options:
Solution:
1991 Upvotes
Verified Answer
The correct answer is:
$m_2 / m_1$
According to law of conservation of linear momentum
$$
\begin{aligned}
& m_1 v_1=m_2 v_2 \quad \ldots \text { (i) } \\
& E_1=\frac{1}{2} m_1 v_1^2, E_2=\frac{1}{2} m_2 v_2^2 \\
& \therefore \frac{E_1}{E_2}=\frac{\frac{1}{2} m_1 v_1^2}{\frac{1}{2} m_2 v_1^2}=\frac{\left(m_1 v_1\right)^2}{\left(m_2 v_2\right)^2} \times \frac{m_2}{m_1} \\
& \therefore \frac{E_1}{E_2}=\frac{m_2}{m_1}
\end{aligned}
$$
$$
\begin{aligned}
& m_1 v_1=m_2 v_2 \quad \ldots \text { (i) } \\
& E_1=\frac{1}{2} m_1 v_1^2, E_2=\frac{1}{2} m_2 v_2^2 \\
& \therefore \frac{E_1}{E_2}=\frac{\frac{1}{2} m_1 v_1^2}{\frac{1}{2} m_2 v_1^2}=\frac{\left(m_1 v_1\right)^2}{\left(m_2 v_2\right)^2} \times \frac{m_2}{m_1} \\
& \therefore \frac{E_1}{E_2}=\frac{m_2}{m_1}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.