Question

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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

Question:-

A cracker o mass 100g explodes into two pieces of equal mass .Show that there two pieces of the cracker fly in opposite direction is V1 = -V2

Answer:-

Given,

$\implies$ Mass of cracker = 100g

$\implies$ Explodes into two equal pieces of mass.

To Find,

$\implies$ To show that these two pieces of the cracker fly in opposite direction that is V1 = -V2.

Solution,

Initial momentum of the cracker is 100g.

After explosion:-

Let,

$\implies$ Mass of first piece = m1

$\implies$ Mass of second piece = m2

After the explosion cracker breaks into two pieces of masses m1 and m2 moving with velocities V1 and v2 then the final momentum of the two pieces are m1 V1 and m2 V2

According to the law of conservation of momentum:-

The momentum of cracker The momentum of cracker

of first piece = of second piece.

For first piece,

We know that,

Momentum = Mass × velocity.

Mass = 50 (M1 = M2 = 50g)

Velocity = V1

Now substituting the given values,

Momentum = 50×V1

Momentum = 50 V1-------(1)

For second piece,

We know that ,

Momentum = Mass × velocity

Mass = 50 (M1 = M2 = 50g)

Velocity = V2

Now substituting the given values,

Momentum = 50×V2

Momentum = 50 V2 ------(2)

As the momentum is conserved,

Final momentum = Initial momentum

$\implies$P = m1v1 + m2v2

$\implies$P = 50 V1 + 50 V2

$\implies$ (-50 V2) = 50 v1

50 gets cancel on both sides,

$\huge{\boxed{-V2 = V1}}$

• It is clear that V1 and V2 are in opposite direction.

• The two pieces m1 and m2 must travel in opposite direction.

Hence ,Proved

-Happies!!

Answer 2

Given,

⟹ Mass of cracker = 100g

⟹ Explodes into two equal pieces of mass.

To Find,

⟹ To show that these two pieces of the cracker fly in opposite direction that is V1 = -V2.

Solution,

Initial momentum of the cracker is 100g.

After explosion:-

Let,

\implies⟹ Mass of first piece = m1

\implies⟹ Mass of second piece = m2

After the explosion cracker breaks into two pieces of masses m1 and m2 moving with velocities V1 and v2 then the final momentum of the two pieces are m1 V1 and m2 V2

According to the law of conservation of momentum:-

The momentum of cracker The momentum of cracker

of first piece = of second piece.

For first piece,

We know that,

Momentum = Mass × velocity.

Mass = 50 (M1 = M2 = 50g)

Velocity = V1

Now substituting the given values,

Momentum = 50×V1

Momentum = 50 V1-------(1)

For second piece,

We know that ,

Momentum = Mass × velocity

Mass = 50 (M1 = M2 = 50g)

Velocity = V2

Now substituting the given values,

Momentum = 50×V2

Momentum = 50 V2 ------(2)

As the momentum is conserved,

Final momentum = Initial momentum

\implies⟹ P = m1v1 + m2v2

\implies⟹ P = 50 V1 + 50 V2

\implies⟹ (-50 V2) = 50 v1

50 gets cancel on both sides,

\huge{\boxed{-V2 = V1}}

−V2=V1

It is clear that V1 and V2 are in opposite direction.

The two pieces m1 and m2 must travel in opposite direction.

Hence ,Proved