Question

A 4kg mass and a 1kg mass are moving with equal kinetic energies.The ratio of their linear momenta is______

• A. 1 : 2
• B. 2 : 1
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is B 2 : 1

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

and linear momentum is given by $P=mv$

so$P=\sqrt{2mK}$

then for two bodies if $K_1:K_2=1:1$ then $P_1:P_2=\sqrt{m_1}:\sqrt{m_2}$

so for given question $P_1:P_2=\sqrt{4}:\sqrt{1}=2:1$

so option B is correct.