Correct Answer  Option 2 : increases by a multiple of n
^{2}
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 ∝ p^{2}
So, if the momentum increases by n times,
⇒ KE ∝ (np)^{2}
⇒ KE ∝ n^{2}p
 Thus, if the momentum of a body is increased by n times, then the kinetic energy increases by a multiple of n2.