Ball A of mass m strikes a stationaty ball B of mass M and undergoes an elastic collision.After collision ball a has a speed one-third of its initial speed.The ratio of M/m is

a.1/4

b.1/2

c.2

d.4

Let the initial velocity of the body of mass m is V.

After collison , it became V/3.

Applying law of conservation of momentum

mV = mV/3 +MV_o(Say)

(Assumption: the direction of the velocity doesnt changes after collison , otherwise not specified)

Then V_o = 2mV/3M----(1)

If the collison is Elastic, then energy remain conserved

=1/2(mV²) = 1/2(m(V/3)²+ MV_o²)

=(mV²) = (m(V/3)²+ MV_o²)

=8/9(mV²) =  MV_o²

^{Substituting value of V_o}

= 8/9(mV²) =  M(4m²V²/9M²)

= 8(m) =  (4m²/M)

= M/m= (1/2)

Note: After collison Speed becomes 1/3 has an incomplete meaning. Direction of ball A should also be specified)

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