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Question

A particle of mass 0.1 kg moving with an initial speed v collides with another particle of same mass kept at rest. If after collision the total energy becomes 0.2 J, then:


A
minimum value of v is 2 m/s
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B
maximum value v is 4 m/s
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C
minimum value v is 3 m/s
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D
maximum value of v is 6 m/s
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Solution

The correct option is A minimum value of v is 2 m/s
The velocities will be $$maximum $$ if the  collision being $$elastic.$$
And in an elastic collision the total  energy remains $$constant.$$
Applying concept of momentum conservation ( because net force on system is zero.) we get $$0.1\times v +0= 0.1\times V_1 + 0.1 \times V_2$$ or $$v=V_1+V_2$$ .............(1)
 because both masses are same.
as this is an elastic collision so  $$e=1$$ where $$e$$ is restitution constant,
given by $$e=\dfrac{V_2-V_1}{u_1-u_1}$$ so $$V_2-V_1=1(v-0)=v$$  ..........(2)
from both equation we get $$2V_2=2v$$ or $$V_2=v$$ and $$V_1=0$$

Or we can say that both masses $$exchanged$$ their velocities.
So the new Kinetic energy is $$E=\dfrac{1}{2}mv^2=0.05\times v^2=0.2Joule $$

so $$v=\sqrt{\dfrac{0.2}{0.05}}=2m/s$$


Physics

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