Question

A cracker of mass 100g explodes into two pieces of equal mass show that these two pieces of the cracker fly in opposite direction that is v1 =-v2

Answer 1

Given :-

▪ A cracker of mass 100 g explodes into two pieces of two pieces ( i.e., each piece is of mass 50 g) .

To Find :-

▪ The two pieces will fly in opposite direction, v₁ = -v₂

Solution :-

According to the law of conservation of momentum the momentum of cracker before and after exploding is is equal.

Before Exploding :

In this case the cracker didn't explode and hence it was at rest so the momentum of the cracker in this case is 0 kg.m/s

After Cracking :

In this case, The cracker exploded into two pieces of equal mass, so we have

Piece 1 :-

• Mass, m = 50 g
• Velocity = v₁

So,

⇒ Momentum = Mass × Velocity

⇒ Momentum = 50 × v₁

⇒ Momentum = 50v₁

Piece 2 :-

• Mass, m = 50 kg
• Velocity = v₂

So,

⇒ Momentum = Mass × Velocity

⇒ Momentum = 50 × v₂

⇒ Momentum = 50v₂

As discussed above, The momentum before and after exploding is same.

⇒ 0 = 50v₁ + 50v₂

⇒ 0 = 50( v₁ + v₂ )

⇒ 0 = v₁ + v₂

⇒ v₁ = - v₂

Hence, Proved.

Answer 2

Given:

• Total mass = 100g
• Devided into Two pieces of equal mass

━━━━━━━━━━━━━━━━

Need to show:

• The two pieces fly in opposite direction with same velocity.

━━━━━━━━━━━━━━━━

Solution:

• Let one mass be m1 and other be m2
• Total mass be= M= 100g

━━━━━━━━━━

As the two masses are equal so,

m1 = m2 = M/2

⟹ m1 = m2 = 100÷ 2g

⟹$\purple{\bold{ m1 = m2 = 50g}}$

━━━━━━━━━━

In a closed system momentum is conserved. Implies $\Delta P=0$

At the beginning,

P= Mass × Velocity

⟹ P = 100 × 0

⟹$\purple{\bold{\boxed{P=0}}}$

━━━━━━━━━━━

As momentum is conserved so

Final momentum = Initial momentum

⟹ P= m1v₁  + m2v₂

⟹ 0 = 50 v₁  + 50v₂

⟹(-50 v₂)= 50v₁ 

⟹ $\red{\bold{\large{\boxed{-{V}_{2}= {V}_{1}}}}}$