Question

Two bodies of masses m1 and m2 have same kinetic energy the ratio of their momentum is

Answer 1

2 answers · Physics 

 Best Answer

A very useful formula for relating kinetic energy (K) to momentum (p) is: 
K = p²/(2m) 

To prove this: 

p = mv 

p² = m²v² 
= m (mv²) 

K = ½mv², therefore mv² = 2K 

p² = m(2K) 

K = p²/(2m) 
___________________________ 

Since the 2 kinetic energies are equal: 
p₁²/(2m₁) = p₂²/(2m₂) 

p₁²/p₂² = m₁/m₂ 

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!