Correct Answer - Option 2 : kinetic energy ∝ (linear momentum)
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The correct answer is option 2) i.e. kinetic energy ∝ (linear momentum)2
CONCEPT:
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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.
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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