Two bodies of masses m1 and m2 have equal momentum their kinetic energies E1 and E2 are in the ratio:
Correct answer: C. m2 : m1
- A. √m1 : √m2
- B. m1 : m2
- C. m2 : m1
- D. √m12 : √m22
Explanation
The kinetic energy of a body is given by the formula: E = 1/2mv^2 where: E is the kinetic energy m is the mass of the body v is the velocity of the body We know that the two bodies have equal momentum, so we have: m1v1 = m2v2 This means that the velocity of the two bodies is in the ratio: v1 : v2 = m2 : m1 The kinetic energy of the two bodies is in the ratio: E1 : E2 = 1/2m1v1^2 : 1/2m2v2^2 Substituting the expression for v1 : v2, we get: E1 : E2 = 1/2m1(m2/m1)^2 : 1/2m2(m1/m2)^2 Simplifying, we get: E1 : E2 = m2 : m1 Therefore, the kinetic energies of the two bodies are in the ratio m2 : m1.
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