Question

A body at rest breaks into two pieces of equal masses. The parts will move
(a) in same direction
(b) along different lines
(c) in opposite directions with equal speeds
(d) in opposite directions with unequal speeds.

Answer 1

(c) in opposite directions with equal speeds

Using the principle of conservation of linear momentum, we can write:
Initial momenta = Final momenta

$$\begin{gathered} \Rightarrow M\times 0=\frac{M}{2}{v}_1+\frac{M}{2}{v}_2 \\ \Rightarrow v_1=-v_2 \end{gathered}$$
where M is the initial mass of the body, at rest.
The final mass of the two pieces moving with equal speeds in opposite direction is equal to $\frac{M}{2}$.