Question

two bodies a and b having mass ratio 1:4 have same kinetic energy which will have higher momentum

Answer 1

Answer:

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Answer 2

Given info : Two bodies A and B having mass ratio 1 : 4 have same kinetic energy.

To find : which will have higher momentum ?

solution : let mass of body A is m, then mass of body B is 4m.

we know, kinetic energy, E = 1/2 mv² ----(1)

and linear momentum, P = mv ---- (2)

from equations (1) and (2) we get,

E = P²/2m

so, P² = 2mE

if kinetic energy remains constant.

P² ∝ m

⇒P₁²/P₂² = m₁/m₂ = m/4m = 1/4

⇒P₁²/P₂² = 1/4 = 1²/2²

⇒P₁/P₂ = 1/2

⇒P₂ = 2P₁

Therefore linear momentum of body B is 2 times as high as that of body A.