Question

A mass of $400\,g$ and a mass of $100\,g$ have same $KE$ , then the ratio of their momentums will be

• A. $2 : 1$
• B. $1 : 2$
• C. $1 : 3$
• D. $3: 1$

Answer 1

Answer: (A)

$2 : 1$

Answer 2

$\frac{p_{1}}{p_{2}}=\sqrt{\frac{2 m_{1} E_{1}}{2 m_{2} E_{2}}}=\sqrt{\frac{2 m_{1}}{2 m_{2}}}$
$\left[\right.$ As $\left.E_{1}=E_{2}\right]$
We have
$\frac{p_{1}}{p_{2}}=\sqrt{\frac{2 m_{1}}{2 m_{2}}}=\sqrt{\frac{m_{1}}{m_{2}}}$
$\therefore \frac{p_{2}}{p_{1}}=\sqrt{\frac{m_{2}}{m_{1}}}$
Here, $m_{2}=400 g , m_{1}=100 g$
$\therefore \frac{p_{2}}{p_{1}}=\sqrt{\frac{400}{100}}=\frac{\sqrt{4}}{1}=\frac{2}{1}$
$\Rightarrow p_{2}: p_{1}=2: 1$