Two solid balls have different radii but are made of same material. The balls are linked together with a long thin thread and released from a large height. At the terminal velocity, the thread is under tension. The larger ball has a fixed mass, but we have choice of the smaller ball with different masses. At what ratio of larger and smaller mass will this tension be maximum?

Answer

`8`

Explanation

`Mg-T-6pietar_(1)v=0`
`mg+T-6pietar_(2)v=0`
`(4/3pi(r_(1)^(3)+r_(2)^(2))xxrhog)/(6pieta(r_(1)+r_(2)))=v`
`v=2/9(r_(1)^(2)-r_(1)r_(2)+r_(2)^(2))(rhog)/eta`
`T=Mg-6^(2)pietar_(1)xx2/9(r_(1)^(2)-r_(1)r_(2)+r_(2)^(2)) (rhog)/eta`
`=4/3pir_(1)^(3)xxrhog-(4pi)/3 rhog[r_(1)^(3)-r_(2)^(2)r_(2)+r_(2)^(2)r_(1)]`
`=4/3pigr[r_(1)^(2)r_(2)-r_(2)^(2)r_(1)]`
`=4/3pirgr_(1)^(2)[r_(2)-(r_(2)^(2))/r_(1)]`
`(dT)/(dr_(2))=0 Rightarrow 4/3 pigr_(1)^(2)[1-(2r_(2))/r_(1)]=0`
`r_(1)=2r_(2)`
`M/m=8`