Question

Two particles with masses in the ratio 1:4 are moving with equal kinetic energies. The magnitude of their linear momentums will conform to the ratio

• A. 1 : 8
• B. 1 : 2
• C. $\sqrt{2}:1$
• D. $\sqrt{2}$

Answer 1

The correct option is B 1 : 2

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

${\left(\frac{v_1}{v_2}\right)}^2=\frac{m_2}{m_1}=4$

$\frac{v_1}{v_2}=2$

$\text{Ratio of linear momentum}=\frac{m_1{v}_1}{m_2{v}_2}$

$=\frac{1}{4}\times 2=\frac{1}{2}$