Two masses of 2 kg and 5 kg are moving with equal kinetic
energies. Find the ratio of magnitudes of respective linear
momenta.
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1/2m₁v₁² =1/2m₂v₂²
2v₁²= 5v₂²
v₁/v₂= √(5/2)
2v₁²= 5v₂²
v₁/v₂= √(5/2)
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K1 = 1/2m₁v₁²
And K2 = 1/2m₂v₂²
As K1 = K2:-
2v₁²= 5v₂²
v₁/v₂= √(5/2)
and m₁/m₂ = 2/5 (GIVEN)
Therefore, (m₁/m₂)(v₁/v₂) = √(5/2) (2/5)
(m₁v₁) / (m₂ / v₂) = √10 / 5
p1 / p2 = √10 / 5 (p1 = m₁v₁, p2 = m₂ / v₂)
And K2 = 1/2m₂v₂²
As K1 = K2:-
2v₁²= 5v₂²
v₁/v₂= √(5/2)
and m₁/m₂ = 2/5 (GIVEN)
Therefore, (m₁/m₂)(v₁/v₂) = √(5/2) (2/5)
(m₁v₁) / (m₂ / v₂) = √10 / 5
p1 / p2 = √10 / 5 (p1 = m₁v₁, p2 = m₂ / v₂)
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