Question

A bomb is thrown vertically upward and it explodes when it reaches its maximum height. After the explosion, it breaks down into two pieces of mass m and 2m. The pieces of mass m and 2m moves in the east and west direction respectively then the centre of mass of the two pieces will:
1. Move towards east
2. Move towards west
3. Remain on the same vertical path as the bomb was moving before explosion
4. Can't say

Answer 1

Correct Answer - Option 3 : Remain on the same vertical path as the bomb was moving before explosion

CONCEPT:

The motion of centre of mass:

• If there is a system of n particles, then the velocity of the centre of mass is given as,

⇒ Mv = m₁v₁ + m2v2 + ... + m_nv_n

• The acceleration of the centre of mass is given as,

⇒ Ma = m1a1 + m2a2 + ... + mnan

\(\Rightarrow Ma=\vec{F_1}+\vec{F_2}+...+\vec{F_n}\)

⇒ Ma = F_ext

• 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.

Conservation of momentum

• If the force applied to the system of particles is zero, then the total momentum of the system of particles will remain conserved.

\(⇒ \vec{P}=\vec{P_1}+\vec{P_2}+...+\vec{P_n}=constant\)

EXPLANATION:

• We know that when a bomb explodes, the forces leading to the explosion of the bomb are only internal forces.
• Since the internal forces contribute nothing to the motion of the centre of mass.
• Therefore the total external force, namely, the force of gravity acting on the body, is the same before and after the explosion.
• Therefore the centre of mass under the influence of the external force continues, therefore, along the same vertical path as it would have followed if there were no explosion. Hence, option 3 is correct.