Question

If a light body and heavy body have same momentum then,
A. they have some kinetic energy.
B. Lighter body have more kinetic energy.
C. Heavier body have more kinetic energy.
D. Cannot be said.

Answer 1

The kinetic energy relation with mass and momentum has to be applied. Momentum is a quantity that describes the motion of a body and kinetic energy is the energy possessed due to motion in a body. The kinetic energy is proportional to the square of momentum divided by mass.

Complete step by step solution:
Given, the momentum is same for both light body and heavy body.
Let the momentum be, $p$.
Let the mass of light body be $m$.
Let the mass of heavy body be $M$.
Let the kinetic energy be ${E_k}$.
The kinetic energy and its relation with momentum is,
${E_k} \propto \dfrac{{{p^2}}}{{2m}}$ …..(1)
Now, since both the body have same momentum, the momentum is constant. Hence the kinetic energy is inversely proportional to the mass.
${E_k} \propto \dfrac{1}{m}$ ……(2)
Hence, for light body the kinetic energy is given as,
${E_k} \propto \dfrac{1}{m}$ ……(3)
For heavy body the kinetic energy is,
${E_k} \propto \dfrac{1}{M}$ ……(4)
Thus from equation (3) and (4) it can be observed that for light body kinetic energy is more and for heavy body the kinetic energy is less.

Hence, the correct option is (B).

Note: The students have to apply the concept of kinetic energy with momentum. If a light body and heavy body have the same momentum, then the lighter body will have more kinetic energy since the velocity has to make up for its lighter mass. Since kinetic energy is inversely proportional to the mass, hence the lighter body will have more kinetic energy.