Question

Two bodies of unequal masses possess the same momentum. Which of the following can be concluded?

• A. Heavier mass possesses lesser K.E.
• B. The masses of the two bodies are in the direct ratio of their velocities
• C. Lighter mass possesses less K.E.
• D. Both (A) and (B)

Answer 1

The correct option is A Heavier mass possesses lesser K.E.

$m_1{v}_1=m_2{v}_2$

$\frac{m_1}{m_2}=\frac{v_2}{v_1}$

If $m_1>m_2\Rightarrow v_2>v_1$

or if $m_1<m_2\Rightarrow v_2<v_1$

$(m_1{v}_1{)}^2=(m_2{v}_2{)}^2$

$\frac{(m_1{v}_1{)}^2}{2}=\frac{(m_2{v}_2{)}^2}{2}$

Now if $m_1>m_2$

$\frac{(m_1{v}_1{)}^2}{2m_1}=\frac{(m_2{v}_2{)}^2}{2m_2}$

$K{E}_1<K{E}_2$