Question

A shell initially at rest explodes into two pieces of equal mass, the two pieces will

• A. move with different velocities in different directions
• B. move with the same velocity in opposite directions
• C. move with the same velocity in the same direction
• D. be at rest

Answer 1

The correct option is B

move with the same velocity in opposite directions

Conservation of linear momentum

If the net external force acting on a system of bodies is zero, then the momentum of the system remains constant.

Since no external force acted on the body, its momentum must be conserved which gives

$$\begin{gathered} initialmomentum=finalmomentum \\ 0=\frac{m}{2}{v}_1+\frac{m}{2}{v}_2 \\ \Rightarrow v_1=-v_2 \end{gathered}$$

where $m$ is the mass of the body initially and $v_1$ is the velocity of the first piece and $v_2$ is velocity of the second piece

therefore the two pieces have equal velocity in opposite directions,

Hence, option B is correct.