Question

help me please solve this question

Answer 1

HELLO THERE!

First, we need to find out a relation between the Kinetic energy and momentum.

We know, Momentum p = mv (m = mass, v = velocity).

From here, we get velocity v = p / m.

Now,

$K.E. = \frac{1}{2}mv^{2}\\\\\\= \frac{1}{2}m\times (\frac{p}{m})^{2}\\\\\\\implies p = \sqrt{2\times K.E. \times m}$

Now,

$K_{1} = K_{2}$

So,

$\frac{p_{1}}{p_{2}} = \frac{2K_{1}m_{1}}{2K_{2}m_{2}}\\\\\\\implies \frac{p_{1}}{p_{2}} = \frac{m_{1}}{m_{2}} = \frac{2}{8} = \frac{1}{4}$

So, the ratio of momentum is 1 : 4.

THANKS!