Question

two bodies of masses M and 2m have equal Kinetic energies what is the ratio of their momenta​

Answer 1

Given:

Masses m and 2m

both masses have equal K.E. ( K.E.₁ = K.E.₂ )

To find:

ratio of momenta, p₁ : p₂

We know that,

$K.E. = \frac {p^{2}}{2m}$

So,

$K.E._{1} = \frac {p_{1}^{2}}{2m}$  and  $K.E._{2} = \frac {p_{2}^{2}}{2(2m)}$

Also, we know that $K.E._{1} = K.E._{2}$,

So,

$\frac {p_{1}^{2}}{2m} = \frac {p_{2}^{2}}{2(2m)}\\\implies \frac {p_{1}^{2}}{p_{2}^{2}} = \frac{1}{2} }\\\implies \frac {p_{1}}{p_{2}} = \frac{1}{\sqrt2} }$

∴ p₁ : p₂ = 1 : √2

Hope this helps! Please mark as Brainliest!