Question

please find the answer thanks

Answer 1

Ratio of masses of the objects = 5:2

So, let first object has the mass of 5m and second be of mass 2m

Let the velocity of first obj be v and second be u

Given that their kinetic energy is same

=> 1/2 × 5m × v² = 1/2 × 2m × u²

Cancel 1/2 and m from both sides as it's common

=> 5v² = 2u²

=> v² = 2u²/5

=> v =
$\sqrt{ \frac{2 {u}^{2} }{5} } \\ \\ = > v = \frac{u \sqrt{2} }{ \sqrt{5} } \\ \\ = > v = u \sqrt{ \frac{2}{5} }$


So, momentum of first object = 5m × v

(mass × velocity)

And momentum of second object = 2m × u

We have to find their ratio. We have derived that, v =
$v = u \sqrt{ \frac{2}{5} }$


So, 5m × v =
$5m \times u \sqrt{ \frac{2}{5} } \\ \\ = m\sqrt{5} \times u \sqrt{2} \\ \\ = mu \sqrt{10}$

So momentum of first object = mu√10

momentum of second object = 2mu

Here it is asked ratio of momentum of B to A
=> ratio of momentum of second obj to first obj

= 2mu : mu√10

cancel mu from both sides

= 2 : √10

=> 2/√10

Further simplifying,

$\frac{2 }{ \sqrt{10} } \\ \\ = \frac{2}{ \sqrt{5 \times 2} } \\ \\ = \frac{ \sqrt{2} }{ \sqrt{5} }$


So answer = √2 : √5


Conclusion :- Ratio is equal to the ratio of roots of their masses.