a light and heavy object have the same momentum.what is their ratio of their kinetic energy?

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Solution

$L e t t h e i r m a s s e s b e : m_{1} & m_{2} t h e i r r e s p e c t i v e v e l o c i t i e s : v_{1} & v_{2} G i v e n m_{1} v_{1} = m_{2} v_{2} m_{1} / m_{2} = v_{2} / v_{1} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) K E (k i n e t i c e n e r g y) K E_{1} / K E_{2} = 1 / 2 * m_{1} {v_{1}}^{2} / 1 / 2 * m_{2} {v_{2}}^{2} f r o m e q 1 w e g e t : K E_{1} / K E_{2} = v_{1} / v_{2} = m_{2} / m_{1}$

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a light and heavy object have the same momentum.what is their ratio of their kinetic energy?

Let their masses be :m1 & m2 their respective velocities :v1 & v2Given m1 v1= m2v2m1/m2= v2/v1 .............................(1)KE(kinetic energy)KE1/KE2 = 1/2 *m1 v12 / 1/2 *m2v22from eq 1 we get :KE1/KE2 = v1/v2 = m2/m1