The relationship between linear momentum and kinetic energy is an important concept in physics. To understand why the correct answer is option 'C', let's break down the relationship between these two quantities and how they are affected by changes in momentum.

**Linear Momentum:**
Linear momentum is the product of an object's mass and its velocity. It is defined as the quantity of motion an object possesses. Mathematically, linear momentum (p) can be expressed as:

p = m * v

where
p is the linear momentum,
m is the mass of the object,
v is the velocity of the object.

**Kinetic Energy:**
Kinetic energy is the energy possessed by an object due to its motion. It depends on both the mass and the velocity of the object. The kinetic energy (KE) of an object can be calculated using the following equation:

KE = (1/2) * m * v^2

where
KE is the kinetic energy,
m is the mass of the object,
v is the velocity of the object.

**Relationship between Linear Momentum and Kinetic Energy:**
The relationship between linear momentum and kinetic energy can be understood by comparing their respective equations. Notice that the mass term is the same in both equations. However, the velocity term in the kinetic energy equation is squared, while the velocity term in the linear momentum equation is not.

This means that changes in velocity will have a greater impact on kinetic energy than on linear momentum. When the velocity of an object increases, its kinetic energy increases at a greater rate compared to its linear momentum.

**Explanation of the Correct Answer:**
In the given question, it is stated that the linear momentum is increased by 50%. Let's assume the initial linear momentum is p1 and the final linear momentum after the increase is p2. Using the given information, we can write:

p2 = p1 + (50/100) * p1
= p1 + 0.5 * p1
= 1.5 * p1

Since linear momentum is directly proportional to velocity, we can write:

p1 = m * v1
p2 = m * v2

where
m is the mass of the object,
v1 is the initial velocity,
v2 is the final velocity.

From the above equations, we can see that the final velocity (v2) is 1.5 times the initial velocity (v1).

Now, let's calculate the initial kinetic energy (KE1) and the final kinetic energy (KE2) using the kinetic energy equation:

KE1 = (1/2) * m * v1^2
KE2 = (1/2) * m * v2^2

Substituting v2 = 1.5 * v1 into the equation for KE2, we get:

KE2 = (1/2) * m * (1.5 * v1)^2
= (1/2) * m * (2.25 * v1^2)
= 2.25 * (1/2) * m * v1^2
= 2.25 * KE1

Thus, the final kinetic energy (KE2) is 2.25 times the initial kinetic energy (KE1). This corresponds to an increase of 125% (2.25 - 1 = 1.25, or 125/100) in