The friction coefficient between the horizontal surface and each of the blocks shown in the figure is 0.20. The collision between the blocks is perfectly elastic. Find the separation between the two blocks when they come to rest. Take `g=10 m/s^2`.

Answer

`50cm`

Explanation

`a= mug=(.2)(10)=2m//s^(2)`.
`v^(2)=1^(2)-2(2)((16)/(100))=1-(16)/(25)=(9)/(25)`
`:. v=3//5m//s`
cons. of linear momentum `rArr 2(3//5)=2(v_(1))+4v_(2)`
`:. v_(1)+2v_(2)=3//5 ......(1)`
`e=1rArr3//5=v_(2)-v_(1) .....(2)`
`(1)` and `(2) =3v_(2)=6//5`
`=v_(2)=2//5m//s`
and `v_(1)=v_(2)-3//5=(2)/(5)-(3)/(5)=-(1)/(5)m//s`
`x_(2)=` Distance covered by `4kg` block `=((2//5)^(2))/(2(2))=(4)/(100)m=4cm`
`x_(1)=` Distance covered by `2kg` block in left direction `=(1)/(100)m =1cm`
Hence `X=x_(1)+x_(2)=5cm`.