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Question

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


A
1 : 2
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B
2 : 1
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C
1 : 4
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D
4 : 1
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Solution

The correct option is B 2 : 1
kinetic energy is given by $$K=\frac{1}{2}mv^2$$
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 $$P_1:P_2=\sqrt4:\sqrt1 =2:1$$
so option B is correct.

Physics

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