Question

If two identical object have equal mass but the momentum of first is two times the another, find the ratio of K.E.​

Answer 1

Let the objects be A & B

Let their masses be m.

Let velocity of A be v and of B be u.

(p is momentum)

p(of A) =mv

p(of B) = mu

p(A):p(B) =2:1

mv:mu = 2:1

mv/mu =2

v/u = 2

so v = 2u.

K.E of A = 1/2 mv²

K.E of B = 1/2 mu²

K.E(A)/K.E(B)= (1/2 mv²)/(1/2 mu²)

= v²/u²

=> K.E(A)/K.E(B)=(2u)²/u²

=> K.E(A)/K.E(B)=4u²/u²

=> K.E(A)/K.E(B)=4/1

=> K.E(A):K.E(B)=4:1

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