Momentum comparison at equal kinetic energy: Two masses m1 and m2 (m1 > m2). Condition: Kinetic energies of both bodies are equal. Choose the correct comparison of their momenta.
Mechanical Engineering
Engineering Mechanics
Difficulty: Easy
Choose an option
Answer
Correct Answer: Momentum of m1 is greater than momentum of m2
Explanation
Given data
- m1 > m2 and K1 = K2.
Concept/Approach For a body: K = p2 / (2m) ⇒ p = √(2mK).
Step-by-step calculation p1 = √(2 m1 K), p2 = √(2 m2 K). Since m1 > m2 and K is common, √(m1) > √(m2). Therefore p1 > p2.
Common pitfall Assuming equal KE means equal momentum — only true if masses are equal.
Final Answer Momentum of m1 is greater than momentum of m2