Question

Two bodies of masses m1 and m2 have equal kinetic energy what is the ratio of their linear momentum

Answer 1

Let m1 have velocity v1. So KE1 = (1/2)(m1)(v1)^2 and linear momentum = (m1)(v1) = p1

Let m2 have velocity v2. So KE2 = (1/2)(m2)(v2)^2 and linear momentum = (m2)(v2) = p2

KE1 = KE2

(1/2)(m1)(v1)^2 = (1/2)(m2)(v2)^2

(m1)(v1)(v1) = (m2)(v2)(v2)

(p1)(v1) = (p2)(v2)

p1/p2 = 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!