Question

A cannon and a supply of cannon balls are inside a sealed rail road car. The cannon fires to the right, and the car recoils to the left. The cannon balls remain in the car after hitting the far wall. Find the maximum distance by which the rail road car move assuming it starts from the rest.

• A. $\frac{L}{2}$
• B. $L$
• C. $0$
• D. Can't determine

Answer 1

The correct option is B $L$

Initially, the whole system is at rest, so $v_{CM}=0$. As there is no external force acting on the system, ${\overrightarrow{v}}_{CM}$ = constant = 0. So position of centre of mass of system remains fixed.
$x_{CM}=\frac{m{x}_1+M{x}_2}{m+M}$ …… (i)
where m is mass of the cannon balls and M that of the (car + cannon) system.
As $\Delta x_{CM}=0$, therefore m $\Delta x_1+M\Delta x_2=0$ …… (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 $\Delta x_2=D$ (say) relative to the ground, opposite to the displacement of the balls; then the displacement of balls relative to ground will be
$\Delta x_1=L-D$ …… (iii)
Substituting the value of $\Delta x_1$ from Equation (iii) in Equation (ii), we get
$m(L-D)-MD=0$
$\Rightarrow D=\frac{mL}{M+m}=\frac{L}{1+\frac{M}{m}}$
$\Rightarrow D<L$
i.e. rail road car cannot travel more than L.