An object of mass `m_(1)` initially moving at speed `v_(0)` collides with an stationary abject of mass `m_(2)= alpham_(1)`, where `a lt 1`. The collision could be completely elastic, completely inelastic, or partially inelastic. After the collision the two objects move at speeds `v_(1) " and " v_(2)`. Assume that the collision is one dimensional , and that object one cannot pass through object two. After the collision, the speed ratio `r_(1)=v_(1)//v_(0)` of object 1 is bounded by

Options

A. `(1-alpha)//(1+alpha)ler_(1)le1`
B. `(1-alpha)//(1+alpha)ler_(1)le1//(1+alpha)`
C. `alpha//(1+alpha)ler_(1)le1`
D. `1//(1+alpha)ler_(1)le2//(1+alpha)`

Answer

B

Explanation

`V_(1)=((M_(1)-eM_(2))/(M_(1)+M_(2)))u_(1)+((1+e)M_(2)u_(2))/((M_(1)+M_(2)))=((1-ealpha))/((1+alpha))V_(0)`
`r_(1)=(V_(1))/(V_(0))=((1-ealpha))/((1+alpha))`
`(r_(1))_("min")=((1-alpha))/((1+alpha))`
`(r_(1))_("max")=((1)/(1+alpha))`