Question

Two bodies of mass 1kg and 4kg possess equal momentum .The ratio of KE is
A) 4 : 1 B) 1 : 4 C) 2 : 1 D) 1 : 2

Answer 1

✿ Solution :-

Given ,

• Mass of body₁ = 1kg
• Mass of body₂ = 4kg
• The bodies 1 & 2 have equal momentum

We need to find,

• Ratios of kinetic energies of body 1 & 2

As we know that,

Kinetic energy ( K.E ) = ½ mv²

Let ,

• Kinetic energy of body₁ be K.E₁
• Kinetic energy of body₂ be K.E₂

Now , finding K.E₁ & K.E₂ using the above formula .

• K.E₁ = 1/2 × 1 × v²

➮ K.E₁ = v²

• K.E₂ = 1/2 × 4 × v²

➮ K.E₂ = 2v²

Now , K.E₁ : K.E₂

Substituting the values ,

⇒ v² : 2v²

⇒ K.E₁ : K.E₂ = 1 : 2

Hence , ratio of Kinetic energies = 1 : 2 . So , option D is your answer .

Answer 2

Concept:

Kinetic energy refers to a type of energy that a particle or object in motion possesses. Mathematically gives as- KE = 1/2 mv²

Given:

Mass of 1st body = 1kg

Mass of 2nd body = 4kg

The momentum of two bodies is equal, P1 = P2

Find:

We need to determine the ratio of Kinetic Energy between the two bodies

Solution:

We know, A particle or an item that is in motion has a sort of energy called kinetic energy.

It is mathematically given as, KE = 1/2 mv² where m is the mass, v is the velocity and KE is the kinetic energy

We know, momentum, P = mv where P is the momentum

Therefore, the equation for kinetic energy becomes,

KE = P²/2m

Therefore, for 1st body kinetic energy becomes-

KE₁ = P₁²/2m₁

For 2nd body kinetic energy becomes-

KE₂ = P₂²/2m₂

Therefore,

KE₁/KE₂ = P₁²/2m₁ × 2m₂/P₂²

It is given that P₁ = P₂

Therefore, KE₁/KE₂ = m₂/m₁

KE₁/KE₂ = 4/1

Thus, the ratio of kinetic energy is 4:1.

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