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
• B. maximum value v is 4 m/s
• C. minimum value v is 3 m/s
• D. maximum value of v is 6 m/s

Answer 1

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 $e=\frac{V_2-V_1}{u_1-u_1}$ 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 $E=\frac{1}{2}m{v}^2=0.05\times v^2=0.2Joule$

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