Question

A body at rest explodes into two equal fragments. The fragments will
1. move in opposite direction with same magnitude of velocity
2. move along different lines
3. move with the same speed
4. none of the above

Answer 1

Correct Answer - Option 1 : move in opposite direction with same magnitude of velocity

The correct answer is option 1) i.e. move in the opposite direction with the same magnitude of the velocity

CONCEPT:

• Momentum: Momentum is the impact due to a moving object of mass m and velocity v.

The momentum (p) of an object is expressed as:

p = mv

• Law of conservation of momentum: Momentum is conserved for any interaction between two objects occurring in an isolated system.
  • ​The conservation of momentum can be observed by analyzing the momentum of the total system or by analyzing the change in momentum.
  • This is done by equating the momentum before the interaction to the momentum after the interaction.

​EXPLANATION:

• An explosion occurs due to internal forces. Hence, the net force on the body is zero and momentum is conserved.
• Considering the case of before explosion and after the explosion, since the body was at rest - momentum before the explosion is zero.
• Therefore, momentum after the explosion will be zero from the law of conservation of momentum.

If m₁ and m₂ are the masses of two fragments and their velocity is v₁ and v₂, 

⇒ m₁v₁ + m₂v₂ = 0

Since the body split into equal fragments, m₁ = m₂

⇒ v₁ + v₂ = 0

⇒ v₁ = -v₂

• Therefore, the fragments will move in opposite direction with same magnitude of velocity.