Two masses of 1g and 9g are moving with equal kinetic energy. The ratio of the magnitudes of their respective linear momenta is

Concept:

Kinetic Energy:

The energy possessed by a particle by the virtue of its motion is called kinetic energy. It is given by

​

Linear momentum:

It is defined as the product of the mass of an object (m) and its velocity (v). It is a vector quantity.​

⇒ P = mv   

where KE = kinetic energy, P = linear momentum, m = mass and v = velocity.

Calculation:

​Given:

Mass of first body m₁ = 1g, Mass of second body m₂ = 9g

The kinetic energy of both the masses is same

Here KE₁ is the kinetic energy of the first body, KE₂ is the kinetic energy of the second body.

v₁ velocity of the first body and v₂ is the velocity of the second body.

∴ KE₁ = KE₂

∴ v₁ = 3v₂   ------ (1)

Now Ratio of the magnitude of their respective linear momentum is given as

Hence the ratio of the magnitude of their linear momenta is 1 : 3.