Search any question & find its solution
Question:
Answered & Verified by Expert
Two bodies of masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ have equal momentum. Then, the ratio of their kinetic energies is
Options:
Solution:
1113 Upvotes
Verified Answer
The correct answer is:
$2: 1$
Let $m_{1}$ be the mass of 1 st body , $m_{1}=1 \mathrm{~kg}$ $m_{2}$ be the mass of $2 \mathrm{nd}$ body, $m_{2}=2 \mathrm{~kg}$
The relation, between kinetic energy and momentum is given by
$$
K=\frac{1}{2} m v^{2}=\frac{p^{2}}{2 m}
$$
where, $p$ is the momentum of the body. Since, momentum of both bodies are same.
Hence, $\frac{k_{1}}{k_{2}}=\frac{p^{2}}{2 m_{1}} \times \frac{2 m_{2}}{p^{2}}$
$$
\frac{k_{1}}{k_{2}}=\frac{2}{1}
$$
Thus, the ratio of their kinetic energies is $2: 1$.
The relation, between kinetic energy and momentum is given by
$$
K=\frac{1}{2} m v^{2}=\frac{p^{2}}{2 m}
$$
where, $p$ is the momentum of the body. Since, momentum of both bodies are same.
Hence, $\frac{k_{1}}{k_{2}}=\frac{p^{2}}{2 m_{1}} \times \frac{2 m_{2}}{p^{2}}$
$$
\frac{k_{1}}{k_{2}}=\frac{2}{1}
$$
Thus, the ratio of their kinetic energies is $2: 1$.
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.