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.

Question

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.

Knowee AI · Accepted Answer