Question

A light and a heavy object have the same momentum. Find out ratio of their kinetic energy. which one has a larger kinetic energy.

Answer 1

Hi...☺

Here is your answer...✌

Let the light object has mass and velocity be m and v respectively
And, heavy object has mass and velocity be M and V respectively

They have same momentum

mv = MV

v/V = M/m ____(1)

Now,

KE1: kinetic energy of Lighter object
KE2 : Kinetic energy of heavier object

Ratio of their Kinetic energy,

$\frac{KE1}{KE2} = \frac{ \frac{1}{2}m {v}^{2} }{ \frac{1}{2} MV {}^{2} } \\ \\ = \frac{m}{M} \times ( \frac{v}{V} ) ^{2} \\ \\ = \frac{m}{M} \times( \frac{M}{m} ) {}^{2} \: & From\: (1)\\ \\ = \frac{ M }{m}$

Since, M>m

•°• KE1 > KE2

Hence,
Kinetic energy of lighter object is greater than kinetic energy of heavier object

Thank you⭐