Question

Two unequal masses possess the same K.E. Then, the heavier mass has

• A. greater momentum.
• B. smaller momentum.
• C. the same momentum as the lighter mass.
• D. greater speed.

Answer 1

The correct option is A greater momentum.

Let, $m_1$<$m_2$
$K.E=\frac{1}{2}{m}_1{v}_1^2$$=$$\frac{1}{2}{m}_2{v}_2^2$
$\frac{m_1}{m_2}=\frac{v_2^2}{v_1^2}$

Since, $m_1$<$m_2$, $\frac{m_1}{m_2}<1$
So, $\frac{v_2^2}{v_1^2}<1$
$p=mv$
$m_1{v}_1^2$$=$$m_1{v}_2^2$
$p_1$$v_1$$=$$p_2$$v_2$
$p_1$/$p_2$$=$$v_2$/$v_1$

Since, $v_2$<$v_1$,$v_2$/$v_1$<1
So, $\frac{p_1}{p_2}<1$
$\Rightarrow p_1$<$p_2$
Thus, this shows that heavier mass has higher momentum.