# If the momentum of a body is increased by n times, then the kinetic energy-

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If the momentum of a body is increased by n times, then the kinetic energy-
1. decreases by a multiple of n
2. increases by a multiple of n2
3. decreases by a multiple of 0.5n
4. increases by a multiple of 0.5n2

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Correct Answer - Option 2 : increases by a multiple of n2

The correct answer is option 2) i.e. increases by a multiple of n2

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:

We know, $KE =\frac{1}{2} mv^2$

Multiplying and dividing by m we get,

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

⇒ KE ∝ p2

So, if the momentum increases by n times,

⇒ KE ∝ (np)2

⇒ KE ∝ n2p

• Thus, if the momentum of a body is increased by n times, then the kinetic energy increases by a multiple of n2.