Question

5. Two bodies of equal masses move with uniform velocities v and 3 v respectively. Find the ratio of their
kinetic energies
[Ans. 9:1]
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Answer 1

Given :

Two bodies of equal masses move with uniform velocities v and 3v respectively.

To Find :

Ratio of their kinetic energies.

Solution :

❖ Kinetic energy is an energy which a body possesses by virtue of being in motion$.$

• It is a scalar quantity having only magnitude.
• SI unit : J

Kinetic energy of body of mass m moving at a velocity of v is given by

• k = 1/2 mv²

♦ Kinetic energy of first body :

➙ k₁ = 1/2 mv²

♦ Kinetic energy of second body :

➙ k₂ = 1/2 m (3v)²

➙ k₂ = 9/2 mv²

By taking the ratio;

➛ k₁ / k₂ = (1/2 mv²) / (9/2 mv²)

➛ k₁ : k₂ = 1 : 9

Answer 2

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Given :

Two bodies of equal masses move with uniform velocities v and 3v respectively.

To Find :

Ratio of their kinetic energies.

Solution :

❖ Kinetic energy is an energy which a body possesses by virtue of being in motion..

• It is a scalar quantity having only magnitude.
• SI unit : J
• Kinetic energy of body of mass m moving at a velocity of v is given by

• k = 1/2 mv²

♦ Kinetic energy of first body :

➙ k₁ = 1/2 mv²

♦ Kinetic energy of second body :

➙ k₂ = 1/2 m (3v)²

➙ k₂ = 9/2 mv²

By taking the ratio;

➛ k₁ / k₂ = (1/2 mv²) / (9/2 mv²)

➛ k₁ : k₂ = 1 : 9