Question

Two unequal masses possess the same momentum, then the kinetic energy of the heavier mass is ...................... the kinetic energy of the lighter mass.

• A. same as
• B. greater than
• C. smaller than
• D. much greater than

Answer 1

Answer: (C)

smaller than

Let us assume $m_1$ is heavier mass.

$P_1=m_1.v_1$ amd $P_2=m_2.v_2$

As we know $P_1=P_2$ then $\frac{m_1}{m_2}=\frac{v_2}{v_1}$

K.E.=$\frac{1}{2}m{v}^2$ so $\dfrac{K.E._1}{K.E._2}=\dfrac{m_1(v_1)^2}{m_2(v_2)^2}$

Then as we know $\frac{v_1}{v_2}=\frac{m_2}{m_1}$ so $\frac{K.E{.}_1}{K.E{.}_2}=\frac{m_2}{m_1}$

As we know m1 is greater mass so $K.E{.}_1$ is smaaler of the two.