A.spring is compressed between two toy carts of masses m1and m2 . when the toy carys are released , the spring exerts on each toy cart equal and opposite forces for the same time t. if the coefficient of friction meu between the ground and the toy-carts is equal the displacements of toy carts are in the ratio

let the displacements be s1 and s2  coefficient of friction=U
frictional force=UR=Umg
                     or,ma=Umg
                    or,a=Ug
v^2=u^2+2as (u=o)
v=sqrt(2as)
now since they exert equal but opposite force so 
F1  = - F2
or,change in momentum of m1= - change in momentum of m2
or m1*v1= -m2*v2 (time cancels)
or m1*sqrt(2as1) = - m2*sqrt(2as2)
squaring,
m1^2 * 2as1 =  - m2^2 2as2
so s1/s2=-(m2^2.m1^2)