a solid iron ball A of radius r collides head on with another stationary solid iron ball B of radius 2r.The ratio of their speeds just after collision (e=0.5)is

Let,  density constant

so,  mass directly proportional to  r³

so ,  m₁ =  4/3 ∏r³ρ = m

       m₂ =   4/3∏8r³ρ = 8m

now , momentum consurvation ,    mv = mv₁+8mv_{2 ,  v1 +8v2 = v}

                                                 0.5 = v₂ - v₁ / v ,  v2 - v1  = 0.5v

so,                                             9v2 = 1.5 v   ,    v2 = 1.5v / 9

                                                 v1 = 1.5v/9 - 0.5v = - 3v /9

v1/v2 = magnitude ratio  =  3v/1.5v   = 2

Thanks Regards
Amar Kumar
AskIITians Faculty
M.tech, IIT Delhi

Let, density constantso, mass directly proportional to r3so , m1 = 4/3 ∏r3ρ = m m2 = 4/3∏8r3ρ = 8mnow , momentum consurvation , mv = mv1+8mv2 , v1 +8v2 = v 0.5 = v2 - v1 / v , v2 - v1 = 0.5v so, 9v2 = 1.5 v , v2 = 1.5v / 9 v1 = 1.5v/9 - 0.5v = - 3v /9v1/v2 = magnitude ratio = 3v/1.5v = 2