Question

Two particle moves M1 and M2 with equal kinetic energy. the ratio of magnitude of their momenta
Option a) m1: m2
B) m2: m1
C) √m1: √m2

Answer 1

option A is correct.

The ratio of linear momenta of two bodies of differing masses possesing equal kinetic energy is the reciprocal of the ratio of their velocities.

We can represent the ratio of their linear momenta in terms of the masses of the bodies using the ratio of the masses as obtaibed above.

M/m=v2/V1

Answer 2

Hey there!

Given,

Two bodies m1 and m2

Let the velocity of 1st body be = v1

Then its Kinetic energy = p²/2m1=(m1v1)²/2m2

Let the velocity of 2nd body be = v2

Then its Kinetic energy = p²/2m2 = (m2v2)²/2m2

Now, (m1v1)²/2m1 = (m2v2)²/2m2

 ∴(m1v1)/(m2v2) = $\frac{ \sqrt{2m2} }{ \sqrt{2m1} }$

Then Ratio = √(2m2) : √(2m1)

Hope It Helps You!