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Question

Two masses 1 kg and 4 kg are moving with equal kinetic energies. The ratio of  magnitudes of their linear momentum is 


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

The correct option is A 1:2
Let the velocity be $$v_1\ and\ v_2$$

$$K.E_1=\dfrac{mv^2}{2}=\dfrac{1\times v_1^2}{2}$$

$$K.E_2=\dfrac{mv^2}{2}=\dfrac{4\times v_2^2}{2}$$

now $$K.E_1=K.E_2$$
so we get $$v_1=2v_2$$

now ratio of momentum ratio ,$$n=\dfrac{1\times v_1}{4\times v_2}=\dfrac{2v_2}{4v_2}$$ 

so $$n=\dfrac{1}{2}$$

Physics

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