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The masses of two substances are 25gm and 89gm respectively.If their kinetic energies are the same the the ratio of momentum is?

Let, m1 = 25 g and its speed be v1. And m2 = 89 g and its speed be v2.

Their KE are same, so,

½ m1(v1)2 = ½ m2(v2)2

=> (m1v1)2/m1 = (m2v2)2/m2

=> (m1v1) : (m2v2) = (m1)1/2 : (m2)1/2

=> (m1v1) : (m2v2) = √25 : √89

=> (m1v1) : (m2v2) = 5 : √89

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 1/2 m1v1 * v1 = 1/2 * m2* v2*v2

25 * v1 * v1 = 89 * v2 * v2

(v1 / v2)2 = 89 / 25

v1 / v2 = root 89 / 5

Ratio of momentum: m1v1 : m2v2

=  25 * root 89  : 89 * 5

= 25root 89 : 445

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