Two bodies of masses m1 and m2 have same kinetic energy. The ratio of their momentum is

The kinetic energy (K.E) of a body is given by the formula K.E = 1/2 mv^2, where m is the mass and v is the velocity of the body.

Given that the two bodies have the same kinetic energy, we can write:

1/2 m1v1^2 = 1/2 m2v2^2

This simplifies to:

m1v1^2 = m2v2^2

Taking the square root of both sides to solve for the velocities, we get:

v1 = sqrt(m2/m1) * v2

The momentum (p) of a body is given by the formula p = mv. Substituting the velocities we found into this formula, we get:

p1 = m1 * sqrt(m2/m1) * v2 = sqrt(m1*m2) * v2 p2 = m2 * v2

Therefore, the ratio of their momenta (p1/p2) is:

p1/p2 = sqrt(m1*m2) * v2 / (m2 * v2) = sqrt(m1/m2)

So, the ratio of their momenta is the square root of the ratio of their masses.