Two bodies of masses m1 & m2 have the same linear momentum. What is the ratio of their kinetic energies?None of these

Let's solve the problem step by step:

Step 1: Recall the formula for linear momentum: Linear momentum (p) = mass (m) × velocity (v)

Step 2: Given that the two bodies have the same linear momentum, we can write the equation as: m1 × v1 = m2 × v2

Step 3: Divide both sides of the equation by m1: v1 = (m2/m1) × v2

Step 4: The kinetic energy (K) of an object is given by the formula: K = (1/2) × m × v^2

Step 5: Substitute the expression for v1 from Step 3 into the kinetic energy formula for m1: K1 = (1/2) × m1 × [(m2/m1) × v2]^2

Step 6: Simplify the equation: K1 = (1/2) × m1 × (m2/m1)^2 × v2^2 K1 = (1/2) × m2^2/m1 × v2^2

Step 7: Repeat the same steps for the kinetic energy of m2: K2 = (1/2) × m2 × v2^2

Step 8: Find the ratio of their kinetic energies: K1/K2 = [(1/2) × m2^2/m1 × v2^2] / [(1/2) × m2 × v2^2] K1/K2 = m2/m1

Therefore, the ratio of their kinetic energies is m2/m1.