Question

A shell at rest explodes. The center of mass of the fragments
(a) Moving along a parabolic path.
(b) Moves along a straight line
(c) Moves along an elliptical path.
(d) Remains at rest.

Answer 1

We will consider linear momentum for such conditions. Because any explosion or collision of any object will give the result of its center of mass as same as it was before the action. And this totally depends upon linear momentum only.

Formula used:
$\overrightarrow{P}=m\overrightarrow{v}$ where v is velocity, P is momentum and m is mass.

Complete step by step answer:
Linear momentum: A linear momentum includes mass as well as object’s velocity so, when we calculate linear momentum we always take the product of mass of an object and its velocity. We define its S.I. unit by kg m/s. Numerically, we can write it as $\overrightarrow{P}=m\overrightarrow{v}$. Momentum and velocity are vector quantities and m is a mass.
Center of mass: This is the mass which is focused on the center of a body. If we define this center properly, then we will mean that it is the average of the whole mass of the body which is centered at one point.
According to the question, the shell was at rest first and then it exploded. So, the explosion took no force from the outside. This means as the forces acting on it were inside of the shell so the momentum will be zero. As the linear momentum of the object (here shell) was zero then even after explosion the center of mass will remain zero. Therefore, after the action of explosion of shell into fragments will result into its center of mass at rest.

Hence, the correct option is (d).

Note:
If in the question collision took place instead of explosion, then also the center of mass will remain at rest. This is because any object in an isolated system exerts the same impulse resulting in the same momentum. His will make the whole system conserved after a collision or an explosion. This further gives us the fact that the center of mass will remain at rest in both the cases. Any enclosure will contain a non changeable momentum due to the tendency of not getting affected by any external forces.