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The relationship between kinetic energy and linear momentum of an object is
1. kinetic energy ∝ (linear momentum)-1
2. kinetic energy ∝ (linear momentum)2
3. kinetic energy ∝ \(\sqrt{linear \: momentum}\)
4. none of the above

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Correct Answer - Option 2 : kinetic energy ∝ (linear momentum)2

The correct answer is option 2) i.e. kinetic energy ∝ (linear momentum)2

CONCEPT:

  • Kinetic energy is the energy possessed by a moving object. 

Kinetic energy (KE) is expressed as:

\(⇒ KE =\frac{1}{2} mv^2\)

Where m is the mass of the object and v is the velocity of the object.

  • 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

EXPLANATION:

\(⇒ KE =\frac{1}{2} mv^2\)

Multiplying and dividing by m we get, 

\(⇒ KE =\frac{1}{2} mv^2 \times \frac{m}{m} = \frac{p^2}{2m}\)

Therefore, p2 = 2mKE

⇒ KE ∝ p2

Thus, kinetic energy ∝ (linear momentum)2

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