2004 AIPMT Work, Energy and PowerRelation between Kinetic Energy and Momentum Easy Question 1 of 2 in Relation between Kinetic Energy and Momentum

A particle of mass $m_1$ is moving with a velocity $v_1$ and another particle of mass $m_2$ is moving with a velocity $v_2$. Both of them have the same momentum but their different kinetic energies are $E_1$ and $E_2$ respectively. If $m_1 \gt m_2$ then :

A $\dfrac{E_1}{E_2} = \dfrac{m_1}{m_2}$
B $E_1 \gt E_2$
C $E_1 = E_2$
D $E_1 \lt E_2$

The answer is D.

Solution

Kinetic energy in terms of momentum: $E = \dfrac{1}{2}mv^2 = \dfrac{(mv)^2}{2m} = \dfrac{p^2}{2m}$
Both particles have the same momentum p, so $E \propto \dfrac{1}{m}$
$\dfrac{E_1}{E_2} = \dfrac{m_2}{m_1}$
Since $m_1 \gt m_2$, $\dfrac{E_1}{E_2} \lt 1$
$\Rightarrow E_1 \lt E_2$

Concept E = p squared over 2m

Relation between Kinetic Energy and Momentum in past papers

2 questions from this chapter have appeared across 2 exam years.