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If a stationary firecracker explodes into the number of particles, then the centre of mass will:
1. Remain stationary
2. Move in vertical direction
3. Move in parabolic path
4. None of these

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Correct Answer - Option 1 : Remain stationary

CONCEPT:

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

⇒ \(M\vec{a}=\vec{F_1}+\vec{F_2}+...+\vec{F_n}\)

⇒ 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.


EXPLANATION:

  • 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.

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