Question

the masses of a lighter and heavier body are m and m respectively .if they have the same momentum , determine which one has a greater kinetic energy​

Answer 1

Given,

• Mass of lighter body = m,

• Mass of heavier body = M

• Both the bodies have same momentum

To find,

Which body will have higher kinetic energy.

Solution,

Let the velocity of lighter body be $v_{m}$ and that of heavier body be $v_{M}$.

As the momentum of both the bodies is equal, we have the relation.

                                                   $mv_{m} = Mv_{m} \\v_{m} = \frac{Mv_{m}}{m}$

Kinetic energy of lighter body = $\frac{1}{2}*m*v_{m} ^{2}$ $= \frac{1}{2m}*M^{2}*v_{M} ^{2}$

Kinetic energy of heavier body = $\frac{1}{2}*M*v_{M} ^{2}$

On comparing both the kinetic energies, we can see that an extra factor $\frac{M}{m}$ comes in case of lighter body. $\frac{M}{m}$  is greater than one.

Therefore, kinetic energy of lighter body will be greater than heavier body.