Question

Two objects with masses m1 and m2 have the same kinetic energy

Answer 1

Let the bodies have masses m1 and m2 with velocities v1 & v2 respectively making their K.E.s (1/2)m1v1²=(1/2)m2v2²=>v1²/v2²=m2/m1

=>v1/v2=√(m2/m1).Now p1/p2=m1v1/(m2v2)

=>p1/p2=(m1/m2)×(v1/v2)=(m1/m2)×√(m2/m1)

=>p1/p2=√(m1/m2).

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!