Question

A bomb traveling in a parabolic path under the effect of gravity explodes in mid-air. The center of mass of fragments will:

• A. move vertically upwards and then downwards.
• B. move vertically downwards.
• C. move in irregular path.
• D. move in the parabolic path which the un-exploded bomb would have travelled.

Answer 1

The correct option is D move in the parabolic path which the un-exploded bomb would have travelled.

It is rather complicated to derive the equations which show that the center of mass is an important location for a body or collection of bodies. The basic idea is that, because of Newton's third law, all the forces on something (like the bomb) which originate inside the system cancel each other out if you observe the entire system. Also, Newton' second law says that the acceleration of the center of mass of a system is equal to the sum of the external forces on the system divided by the total mass of the system (this is what is complicated to prove). The bomb experiences only gravity as an external force; all the forces which caused it to explode are internal forces and sum to zero if you look at the whole system.

Hence the center of mass of fragments after explosion also moves in the parabolic path.