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A body is projected at an angle with some initial velocity from the surface of the earth and follows the parabolic path. If the body explodes somewhere during the flight and splits into a number of particles, then the centre of mass of the particles will move in:
1. Vertical direction
2. Any direction
3. Same parabolic path
4. None of these

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Correct Answer - Option 3 : Same parabolic path

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 body is projected at an angle with some initial velocity from the surface of the earth and follows the parabolic path.
  • The body explodes somewhere during the flight and splits into a number of particles.
  • When the body explodes only internal forces acts on the body and we know that the internal forces contribute nothing to the motion of the centre of mass.
  • Therefore the centre of mass will follow the same parabolic path after the explosion. Hence, option 3 is correct.

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