Two bodies of mass 2.0 kg and 6.0 kg have equal kinetic energies. What is the exact ratio of their linear momenta p1 : p2?
Answer and explanation
Correct answer: A. 1 : √3
- Step 1: Relate kinetic energy and momentum: K = p² / (2m) => p = √(2mK). Step 2. For equal K: p1 / p2 = √(m1 / m2) = √(2.0 / 6.0) = √(1/3) = 1 / √3. Answer: 1 : √3. Why not the others: 1 : 3 is the mass ratio; 1 : 9 squares the mass ratio; 3 : 1 inverts the ratio.
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