Question

What will be the ratio of momentum sof masses is one of the mass is 10 times heavy as the other have equal kinetic energy?

Answer 1

p₂ = m₂ v₂
p₁ = m₁v₁

now m₁= 10 m₂

10 = m₁ / m₂------------------------------ ( 1) 

K.E ₁ = K.E ₂

i.e.,

1/2 m₁ v₁² = 1/2 m₂ v₂²

m₁ v₁² =m₂ v₂²

10m₂ v₁² = m₂ v₂²

10 = v₂² / v₁² ---------------------------------------- ( 2 ) 

m₁ / m₂ = v₂² / v₁²

multiplying both side by v₁ / v ₂

m₁ v₁ / m₂ v₂ = v₂² v₁/ v₁² /v₂

p ₁ /  p₂ = v₂ / v ₁

p ₁ / p₂ = √ 10 

√10 : 1