a moving sphere p collides with another sphere q at rest,if the collision takes place along the line joining their centre of mass such that their total k.e. is conserved and the fraction of k.e. transferred by the colliding particle is 8/9,the mass p and the mass q bear the ratio of

 let the mass of particle p be Mp and the mass of other particle q be Mq

 let initial momentam of particle Pi 

 aplying conservation of momentam

 Pi + o = Pf + Qf ......1                 ( Pf,Qf are the momentam of P,q after collision)

by using p^2/2m = KE EQ 1 becomes

 sqrt{(KE)pi. Mp}  =  sqrt{(KE)pf. Mp}  + sqrt{(KE)qf.Mq}..........2

 now applying conservation of total kinetic energy

(kinetic energy initially) (KE)pi +0 = (kE)pf  +(kE)qf       (final kinetic energy of p,q)

   from the given data that 8/9 (kinetic energy of particle p) is transferred to particle q so now KE of  p now is 1/9of initial

 so (KE)pf =1/9 (kE)pi..........3

     (KE)qf =8/9 (KE)pi..........4

putting values from 3,4 in eq 2

Mp/Mq =2

 approve my ans if u like

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