The correct option is B L
Initially, the whole system is at rest, so vCM=0. As there is no external force acting on the system, →vCM = constant = 0. So position of centre of mass of system remains fixed.
xCM=mx1+Mx2m+M …… (i)
where m is mass of the cannon balls and M that of the (car + cannon) system.
As ΔxCM=0, therefore m Δx1+MΔx2=0 …… (ii)
As cannon balls cannot leave the car, so maximum displacement of the balls relative to the car is L and in doing so the car will shift a distance Δx2=D (say) relative to the ground, opposite to the displacement of the balls; then the displacement of balls relative to ground will be
Δx1=L−D …… (iii)
Substituting the value of Δx1 from Equation (iii) in Equation (ii), we get
m(L−D)−MD=0
⇒D=mLM+m=L1+Mm
⇒D<L
i.e. rail road car cannot travel more than L.