Correct Answer - Option 1 : Remain stationary
Centre of mass:
- The centre of mass of a body or system of a particle is defined as, a point at which the whole of the mass of the body or all the masses of a system of particle appeared to be concentrated.
The motion of the centre of mass:
- Let there are n particles of masses m1, m2,..., mn.
- If all the masses are moving then,
⇒ Mv = m1v1 + m2v2 + ... + mnvn
⇒ Ma = m1a1 + m2a2 + ... + mnan
⇒ M = m1 + m2 + ... + mn
- Thus, the total mass of a system of particles times the acceleration of its centre of mass is the vector sum of all the forces acting on the system of particles.
- The internal forces contribute nothing to the motion of the centre of mass.
- In the given question a stationary firecracker explodes into a number of particles.
- When the firecracker explodes only internal forces acts on the firecracker and we know that the internal forces contribute nothing to the motion of the centre of mass.
- Therefore the centre of mass will remain stationary after the explosion. Hence, option 1 is correct.