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

kinetic energy is given by $K=\frac{1}{2}m{v}^2$

so $m_1{v}_1^2=m_2{v}_2^2$ then $\frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}$

let $m_1$ is heavier body.

means heavier body has less magnitude of velocity.

as we know linear momentum is given by $P=mv$

then $P_1=m_1{v}_1$ and $P_2=m_2{v}_2$

$\frac{P_1}{p_2}=\frac{m_1{v}_1}{m_2{v}_2}$ $=>$ $\frac{P_1}{P_2}=\frac{m_1}{m_2}\times \sqrt{\frac{m_2}{m_1}}$

so $\frac{p_1}{P_2}=\sqrt{\frac{m_1}{m_2}}$

so it is clear that momentum of heavier object will be more.

so best possible option is A.