Question

A light and a heavy object have the same momentum. Which one of the following statements are correct regarding the kinetic energy of these two objects?

• A. $(K.E{)}_1>(K.E{)}_2$
• B. $(K.E{)}_1=(K.E{)}_2$
• C. $(K.E{)}_1<(K.E{)}_2$
• D. There is no relation between their kinetic energies

Answer 1

The correct option is A

$(K.E{)}_1>(K.E{)}_2$

We know that momentum of a body = mv
where, m = mass of the object and v = velocity of the object
Kinetic Energy, KE = $\frac{1}{2}m{v}^2$=$\frac{1}{2}\frac{m^2{v}^2}{m}$ (multiplying & dividing by m)
= $\frac{1}{2}\frac{{\left(mv\right)}^2}{m}=\frac{p^2}{2m}$
Hence, K.E =$\frac{p^2}{2m}$
Let kinetic energy of heavier and lighter objects be $K.E_1$ and $K.E_2$ respectively.
$\frac{K.E_1}{K.E_2}=\frac{\frac{P^{2}1}{2m1}}{\frac{P{2}^2}{2m2}}=\frac{m2}{m1}(P1=P2)$
Now, m2>m1
$\therefore K.E_1>K.E_2$
Hence, kinetic energy of lighter object is greater than heavier object.