A plank of mass 4m is placed on a smooth horizontal surface and a spring of force constant k is attached to the plank, whose other end is fixed on a block of mass m placed over the plank. All surfaces are smooth. A bullet of mass m moving with horizontal velocity u strikes the block and gets embeded in it. Choose the correct option for subsequent motion :
(A) velocity of plank when spring gets compressed to maximum is u/6
(B) the maximum compression in the spring is √(m/3k)u
(C) the bullet will have velocity relative to plank at the instant of maximum compression
(D) the force exerted by spring on plank will reach a maximum of √(mu2/k)
