Question

A particle of mass $100g$ moving at an initial speed $u$ collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes $0.2J$ after the collision, what could be the minimum and the maximum value of $u$?

• A. m/s, m/s
• B. m/s, m/s
• C. m/s, m/s
• D. m/s, m/s

Answer 1

The correct option is B

m/s, m/s

mass of particle = $0.1kg$

Total K.E. after the collision = $0.2J$

As the zero energy is lost in the case of perfectly elastic collision, and in the case of perfectly elastic

collision of two similar bodies, their velocities are exchanged.

So, $\frac{1}{2}m{u}^2$ = $0.2$

$u$ = $2$ m/s {This is the minimum speed required to get the given K.E.}

Now for maximum velocity, we take the collision to be perfectly inelastic as maximum energy is lost in this type.
According to conservation of linear momentum
$mu+m\left(0\right)=(m+m)vmu=2mvu=2vv=\frac{u}{2}Totalenergy=\frac{1}{2}\left(2m\right)v^2=0.2J=m{v}^2=0.2\frac{m{u}^2}{4}=0.2u^2=\frac{\left(0.2\right)\left(4\right)}{100\times {10}^{-3}}=8u=\sqrt{8}=2\sqrt{2}m/s$